Grade 9 · Math · Algebra 1

9th grade Simplify a square root or cube root worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Simplify a square root or cube root

Grade 9 Math Worksheet - Building Confidence

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

Ari's square rug covers 72 square feet (room for one very sleepy cat). Its side is √72 feet. Pull one number out of each pair: √72 = ?√2. What number goes in front of √2?
Bo's square window for a dollhouse has an area of 48 square inches. Its side is √48 inches. Pull one number out of each pair: √48 = ?√3. What number goes in front of √3?
Esme's square doll quilt covers 200 square inches. Its side is √200 inches. Pull one number out of each pair: √200 = ?√2. What number goes in front of √2?
Jun's square sticky note covers 32 square centimeters. Its side is √32 cm. Pull one number out of each pair: √32 = ?√2. What number goes in front of √2?
Luz's cube-shaped box of buttons holds 192 cubic centimeters (the buttons have no complaints). Pull one number out of each triple: ∛192 = ?∛3. What number goes in front of ∛3?
Milo's big cube-shaped block holds 648 cubic centimeters, so each edge is ∛648 cm. Pull one number out of each triple: ∛648 = ?∛3. What number goes in front of ∛3?
Noah's cube-shaped craft box holds 320 cubic inches, so each edge is ∛320 inches. Pull one number out of each triple: ∛320 = ?∛5. What number goes in front of ∛5?
8.
Pia's robot screen shows √108 and asks for every pair to be pulled out. Which is √108 with every pair pulled out?
- 36√3
- 6√18
- 2√27
- 6√3
9.
Ren's puzzle card shows √112 (the card insists it is not a trick). Which is √112 with every pair pulled out?
- 16√7
- 4√28
- 2√28
- 4√7
10.
The code on Zee's padlock tag is hidden in √300. Which is √300 with every pair pulled out?
- 100√3
- 10√30
- 10√3
- 2√75

9th grade Simplify a square root or cube root worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Simplify a square root or cube root. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can write √72 as 6√2 by pulling one number out of each pair in its strip.
I can simplify a cube root, ∛(-54) = -3∛2, by pulling one number out of each triple.
I can put a front number back inside the root: 7√2 = √98.

Standard: N-RN.A.2

Words to know

strip: A number written as its prime factors in a row: 72 = 2 × 2 × 2 × 3 × 3.

pair: Two equal factors side by side, like 3 × 3.

triple: Three equal factors side by side, like 2 × 2 × 2.

fully simplified: No pair (or triple, for a cube root) is left under the root.

front number: The whole number in front of the root, the 6 in 6√2.

Common mistakes

Your child put the whole square in front of the root, for example 36√2 for √72.

Your child pulled one pair out of the root and stopped while another pair was still inside.

Your child divided the inside by the number out front instead of by its square.

What to say

Ask: what number times itself makes 36?

Ask: is there still a pair of equal factors under the root?

Ask: if 6 comes out of the root, did 6 or 36 leave the inside?

Questions parents ask

What is the most common mistake with simplify a square root or cube root?

Your child put the whole square in front of the root, for example 36√2 for √72.

How can I help my child with simplify a square root or cube root?

Ask: what number times itself makes 36?

Are these 9th 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 algebra 1

See all Algebra 1

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