# 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. $$\sqrt{16}$$ = ____
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. $$\sqrt{64}$$ = ____
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. $$\sqrt{25}$$ = ____
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. $$\sqrt{100}$$ = ____
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. $$\sqrt{1}$$ = ____
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. $$\sqrt{9}$$ = ____
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. $$\sqrt{36}$$ = ____
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. $$\sqrt{81}$$ = ____
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. $$\sqrt{4}$$ = ____
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. $$\sqrt{64}$$ = ____
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. $$\sqrt{36}$$ = ____
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. $$\sqrt{49}$$ = ____
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. $$\sqrt{100}$$ = ____
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. $$\sqrt{25}$$ = ____
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. $$\sqrt{1}$$ = ____
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. $$\sqrt{9}$$ = ____
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. $$\sqrt{4}$$ = ____
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. $$\sqrt{169}$$ = ____
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. $$\sqrt{121}$$ = ____
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. $$\sqrt{400}$$ = ____
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.

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