Grade 7 · Math

7th grade Square roots of perfect squares worksheet

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Square roots of perfect squares

Grade 7 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Zee's math book asks for the positive number x with x² = 225. What is x?
Ari's quiz card says x² = 289, and x is positive. A star sticker is the prize. What is x?
3.
Bo looks for a perfect square on a puzzle card. Only one number is a whole number times itself. Which number is it?
- 26
- 169
- 170
- 168
4.
Esme's math book lists four numbers, and only one is a perfect square, a whole number times itself. Which number is it?
- 30
- 224
- 226
- 225
5.
Jun's robot shows four numbers. Exactly one is a perfect square, a whole number times itself. Which number is it?
- 288
- 289
- 290
- 34
6.
Luz compares √49 with 8 on a sheet of paper. Which statement is true?
- √49 is greater than 8
- They are equal
- 8 is greater than √49
7.
Noah's quiz card compares √169 with 14. A star waits for the right statement. Which statement is true?
- √169 is greater than 14
- 14 is greater than √169
- They are equal
8.
Pia's robot compares √64 with 8 and blinks twice. Which statement is true?
- 8 is greater than √64
- They are equal
- √64 is greater than 8
Zee's math book asks for √225 + 10. The page smells like new paper. What is √225 + 10?
10.
Zee's quiz card compares √81 with 7. One statement is true. Which statement is true?
- √81 is greater than 7
- They are equal
- 7 is greater than √81

7th grade Square roots of perfect squares worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Square roots of perfect squares. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can read √49 as "which number times itself makes 49?" and answer 7.
I can tell a perfect square (169 = 13 × 13) from a number that is only close (168, 170).
I can use a root in a calculation: √(64 + 36), √81 + 5, or the side of a square from its area.

Standard: state-only (CCSS 8.EE.A.2)

Words to know

square root (√): The number that times itself makes the number under the sign. √49 = 7.

perfect square: A whole number times itself: 1, 4, 9, 16, 25 and so on.

square (of a number): A number times itself. 7² = 7 × 7 = 49.

side: One edge of a square. The side times itself is the area.

area: How much flat space a shape covers, in square units.

positive: Greater than 0. Square roots in this pack are positive.

Common mistakes

Your child halved the number under the root sign (√36 as 18). A square root is the number that times itself makes the number: ask which number multiplied by itself gives 36.

Your child squared the number under the root sign (√9 as 81) instead of finding the root. A square root goes the other way: it asks which number times itself makes 9.

Your child picked a number that is one away from a perfect square (168 or 170 for 169). A perfect square is a whole number times itself, so test it: find a number that multiplied by itself gives exactly that number.

Questions parents ask

What is the most common mistake with square roots of perfect squares?

Your child halved the number under the root sign (√36 as 18). A square root is the number that times itself makes the number: ask which number multiplied by itself gives 36.

Are these 7th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 7 math

See all grade 7 math

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