Grade 7 · Math

7th grade Square roots of perfect squares worksheet

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Square roots of perfect squares

Grade 7 Math Worksheet - Building Confidence

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

Read this first
Use this
The same whole number goes in both squares.
Ari's combination padlock tag shows √4, and the strip below asks which whole number fills both squares. What is √4?
Bo's puzzle card asks for √9, with a strip of two equal squares drawn. A gold star waits. What is √9?
Jun's math book asks for √25, with the strip of two equal squares printed. What is √25?
Hint: 10 × 10 = 100 and 12 × 12 = 144. Luz's robot needs √121 to open a door. The hint shows two squares just below and just above 121. What is √121?
Hint: 12 × 12 = 144 and 14 × 14 = 196. Milo's padlock tag shows √169, with a hint about the squares on either side of it. What is √169?
Hint: 16 × 16 = 256 and 18 × 18 = 324. Pia's puzzle card asks for √289, with a hint about two nearby squares. A star sticker is the prize. What is √289?
Use this
The side × itself makes the area.
Ren's square flower bed has an area of 49 square feet, and the bees approve. How long is each side, in feet?
Tala's square tent floor has an area of 81 square feet, with room for one very large pillow. How long is each side, in feet?
Ari sews a square quilt block with an area of 169 square inches. The cat watches closely. How long is each side, in inches?
Bo's dog has a square play pen with an area of 289 square feet. The dog supervises. How long is each side, in feet?

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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