Grade 7 · Math

7th grade Square roots of perfect squares worksheet

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Square roots of perfect squares

Grade 7 Math Worksheet - Challenge Me

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

Tala sews ribbon all around a square blanket with an area of 64 square feet. The blanket is very soft. How many feet of ribbon are needed?
Zee's square plant bed has an area of 196 square feet, with a fence all the way around. The plants wave. How many feet of fence are needed?
Ari's padlock tag says √(64 + 36). Work inside the root first. What is √(64 + 36)?
Esme's math book asks for √(225 + 64). The sum makes a perfect square. What is √(225 + 64)?
“A: 9 B: √100 C: √64 D: 11” Luz's notes list four numbers, and some have square root signs. Write the letters with commas, like P, Q, R, S. What is the order from least to greatest?
“A: √1 B: 3 C: √0 D: √4” Milo's notes list four numbers, and some have square root signs. Write the letters with commas, like P, Q, R, S. What is the order from least to greatest?
Ren's square flower bed has an area of 169 square feet, and a path 2 feet wide goes all around it. How long is each side of the bed with its path, in feet?
Tala's robot shows x² + 5 = 54 and needs the positive number x. What is x?
Zee's math book asks for the positive number n with n² − 9 = 135. What is n?
Ari's quiz card says k² + 20 = 101, and k is positive. A star waits. What is k?

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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