Spectrum Math Grade 8 Chapter 2 Lesson 2 Answer Key Square Roots

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 6², 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.