Students can use the **Spectrum Math Grade 8 Answer Key** **Chapter 2 Lesson 2.2 Square Roots** as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 8 Chapter 2 Lesson 2.2 Square Roots Answers Key

The square of a number is that number times itself. A square is expressed as 6^{2}, which means 6 × 6, or 6 squared. The square root of a number is the number that, multiplied by itself, equals that number. The square root of 36 is 6: = 6.

Not all square roots of numbers are whole numbers like 6. Numbers that have a whole number as their square root are called perfect squares.

The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

is a little more than 7, because is exactly 7. is between 7 and 8 but closer to 8, because 60 is closer to 64 than to 49.

**Identify the square root of these perfect squares.**

a. \(\sqrt{16}\) = ____

Answer: 4

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 16 is 4. \(\sqrt{16}\) = 6.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

b. \(\sqrt{64}\) = ____

Answer: 8

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 64 is 8. \(\sqrt{64}\) = 8.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

c. \(\sqrt{25}\) = ____

Answer: 5

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 25 is 5. \(\sqrt{25}\) = 5.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 2.

a. \(\sqrt{100}\) = ____

Answer: 10

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 100 is 10. \(\sqrt{100}\) = 10.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

b. \(\sqrt{1}\) = ____

Answer: 1

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 1 is 1. \(\sqrt{1}\) = 1.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

c. \(\sqrt{9}\) = ____

Answer: 3

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 9 is 3. \(\sqrt{9}\) = 3.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 3.

a. \(\sqrt{36}\) = ____

Answer: 6

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 36 is 6. \(\sqrt{36}\) = 6.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

b. \(\sqrt{81}\) = ____

Answer: 9

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 81 is 9. \(\sqrt{81}\) = 9.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

c. \(\sqrt{4}\) = ____

Answer: 2

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 4 is 2. \(\sqrt{4}\) = 2.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

**Estimate the following square roots.**

Question 4.

\(\sqrt{85}\) is between ____ and ___ but closer to ____

Answer: \(\sqrt{85}\) is between **9** and **10** but closer to 9.

\(\sqrt{85}\) is between 9 and 10 but closer to 9, because 85 is closer to 81 than to 100.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 5.

\(\sqrt{20}\) is between ____ and ___ but closer to ____

Answer: \(\sqrt{20}\) is between **4** and **5** but closer to 4.

\(\sqrt{20}\) is between 4 and 5 but closer to 4, because 20 is closer to 16 than to 25.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 6.

\(\sqrt{35}\) is between ____ and ___ but closer to ____

Answer: \(\sqrt{35}\) is between **5** and **6** but closer to 6.

\(\sqrt{35}\) is between 5 and 6 but closer to 6, because 35 is closer to 36 than to 25.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 7.

\(\sqrt{70}\) is between ____ and ___ but closer to ____

Answer: \(\sqrt{70}\) is between **8** and **9** but closer to 8.

\(\sqrt{70}\) is between 8 and 9 but closer to 8, because 70 is closer to 64 than to 81.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 8.

\(\sqrt{45}\) is between ____ and ___ but closer to ____

Answer: \(\sqrt{45}\) is between **6** and **7** but closer to 7.

\(\sqrt{45}\) is between 6 and 7 but closer to 7, because 45 is closer to 49 than to 36.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

**Identify the square root of these perfect squares.**

Question 1.

a. \(\sqrt{64}\) = ____

Answer: 8

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 64 is 8. \(\sqrt{64}\) = 8.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

b. \(\sqrt{36}\) = ____

Answer: 6

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 36 is 6. \(\sqrt{36}\) = 6.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

c. \(\sqrt{49}\) = ____

Answer: 7

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 49 is 7. \(\sqrt{49}\) = 7.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 2.

a. \(\sqrt{100}\) = ____

Answer: 10

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 100 is 10. \(\sqrt{100}\) = 10.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

b. \(\sqrt{25}\) = ____

Answer: 5

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 25 is 5. \(\sqrt{25}\) = 5.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

c. \(\sqrt{1}\) = ____

Answer: 1

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 1 is 1. \(\sqrt{1}\) = 1.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 3.

a. \(\sqrt{9}\) = ____

Answer: 3

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 9 is 3. \(\sqrt{9}\) = 3.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

b. \(\sqrt{4}\) = ____

Answer: 2

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 4 is 2. \(\sqrt{4}\) = 2.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

c. \(\sqrt{169}\) = ____

Answer: 13

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 169 is 13. \(\sqrt{169}\) = 13.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 4.

a. \(\sqrt{121}\) = ____

Answer: 11

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 121 is 11. \(\sqrt{121}\) = 11.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

b. \(\sqrt{81}\) = ____

Answer: The square root of a number is the number that, multiplied by itself, equals that number. The square root of 81 is 9. \(\sqrt{81}\) = 9.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

c. \(\sqrt{400}\) = ____

Answer: 20

The square root of a number is the number that, multiplied by itself, equals that number. The square root of 400 is 20. \(\sqrt{400}\) = 20.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

**Estimate the following square roots.**

Question 5.

\(\sqrt{78}\) is between ___ and ___ but closer to ____

Answer: \(\sqrt{78}\) is between **8** and **9** but closer to 9.

\(\sqrt{78}\) is between 8 and 9 but closer to 9, because 78 is closer to 81 than to 64.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 6.

\(\sqrt{108}\) is between ___ and ___ but closer to ____

Answer: \(\sqrt{108}\) is between **10** and **11** but closer to 10.

\(\sqrt{108}\) is between 10 and 11 but closer to 10, because 108 is closer to 100 than to 121.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 7.

\(\sqrt{9}\) is between ___ and ___ but closer to ____

Answer: \(\sqrt{9}\) is between **2** and **3** but closer to 3.

\(\sqrt{9}\) is between 2 and 3 but closer to 3, because 9 is closer to 9 than to 4.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 8.

\(\sqrt{175}\) is between ___ and ___ but closer to ____

Answer: \(\sqrt{175}\) is between **13** and **14** but closer to 13.

\(\sqrt{175}\) is between 13 and 14 but closer to 13, because 175 is closer to 169 than to 196.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 9.

\(\sqrt{3}\) is between ___ and ___ but closer to ____

Answer: \(\sqrt{3}\) is between **1** and **2** but closer to 2.

\(\sqrt{3}\) is between 1 and 2 but closer to 2, because 3 is closer to 4 than to 1.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 10.

\(\sqrt{52}\) is between ___ and ___ but closer to ____

Answer: \(\sqrt{52}\) is between **7** and **8** but closer to 7.

\(\sqrt{52}\) is between 7 and 8 but closer to 7, because 52 is closer to 49 than to 64.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 11.

\(\sqrt{132}\) is between ___ and ___ but closer to ____

Answer: \(\sqrt{132}\) is between **11** and **12** but closer to 11.

\(\sqrt{132}\) is between 11 and 12 but closer to 11, because 132 is closer to 121 than to 144.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 12.

\(\sqrt{80}\) is between ___ and ___ but closer to ____

Answer: \(\sqrt{80}\) is between **8** and **9** but closer to 9.

\(\sqrt{80}\) is between 8 and 9 but closer to 9, because 80 is closer to 81 than to 64.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 13.

\(\sqrt{125}\) is between ___ and ___ but closer to ____

Answer: \(\sqrt{125}\) is between **11** and **12** but closer to 11.

\(\sqrt{125}\) is between 11 and 12 but closer to 11, because 125 is closer to 121 than to 144.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.

Question 14.

\(\sqrt{28}\) is between ___ and ___ but closer to ____

Answer: \(\sqrt{28}\) is between **5** and **6** but closer to 5.

\(\sqrt{28}\) is between 5 and 6 but closer to 5, because 28 is closer to 25 than to 36.

Numbers that have a whole number as their square root are called perfect squares. The expression of a square root is called a radical. The symbol is called a radical sign. When a number is not a perfect square, you can estimate its square root by determining which perfect squares it comes between.