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 - Challenge Me

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

In math club, Esme meets ∛(-432). Esme simplifies it fully, as a whole number times a cube root. What whole number is in front?
Jun's padlock tag shows ∛(-16). Jun simplifies it fully, as a whole number times a cube root. What whole number is in front?
Kira simplifies √(x^9) for x ≥ 0 by pulling each pair x × x out of the root. The answer is x to a power times √x. What is that power?
In math club, Luz simplifies √(x^7) for x ≥ 0, one pair of x at a time. The answer is x to a power times √x. What is that power?
Milo's robot simplifies √(x^11) for x ≥ 0 (it loves pairs, like socks). The answer is x to a power times √x. What is that power?
Noah's math book shows √(x^5) for x ≥ 0. The answer is x to a power times √x. What is that power?
Pia wants 7√2 written as one root, √n, with nothing in front. What is n?
Ren's robot only reads single roots, so 4√6 must become √n. What is n?
In math club, Tala rewrites 3√11 as one root, √n. What is n?
Zee's padlock opens with the number n in √n = 2√13. What is n?

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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