Grade 9 · Math · Algebra 1

9th grade Simplify a square root or cube root worksheet

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Simplify a square root or cube root

Grade 9 Math Worksheet

NameDate

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

Ari's square play mat covers 180 square inches, so its side is √180 inches. Ari simplifies √180 fully, so no pair is left inside. What whole number is in front of the root?
Bo's puzzle card shows √243. Bo simplifies √243 fully, so no pair is left inside. What whole number is in front of the root?
Esme's square window has an area of 80 square inches, so its side is √80 inches. Esme simplifies √80 fully, so no pair is left inside. What whole number is in front of the root?
Jun's square quilt patch covers 175 square centimeters (one patch, many opinions). Jun simplifies √175 fully, so no pair is left inside. What whole number is in front of the root?
In math club, Kira simplifies √252 fully, so no pair is left inside the root. What whole number is left inside the root?
Milo simplifies √450 fully on a worksheet (in pencil, just in case). What whole number is left inside the root?
Noah's padlock code is the number left inside √500 once it is fully simplified. What whole number is left inside the root?
8.
Pia's math book has √360 in a puzzle. Which is √360 fully simplified?
- 6√60
- 36√10
- 2√90
- 6√10
9.
Tala's robot screen shows √600. Which is √600 fully simplified?
- 10√6
- 100√6
- 10√60
- 2√150
10.
In math club, Zee simplifies √720 on the board. Which is √720 fully simplified?
- 2√180
- 144√5
- 12√5
- 12√60

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

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

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.

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.

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?

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.

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