Grade 9 · Math · Algebra 1

9th grade Simplify square roots with letters or a fraction inside worksheet

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Simplify square roots with letters or a fraction inside

Grade 9 Math Worksheet - Challenge Me

NameDate

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

Ari's robot simplifies √(75x^4) for x > 0 (it hums while it works). Fully simplified, what whole number is in front?
Bo simplifies √(147x^6) for x > 0 in math club. Fully simplified, what whole number is in front?
Esme's puzzle card shows √(128x^2) for x > 0. Fully simplified, what whole number is in front?
4.
Jun simplifies √(x⁶/(4y²)) for positive x and y. Which is right?
- x⁶/(2y)
- x³/(4y)
- x³/(2y)
5.
Luz simplifies √(a²b⁴/(9c⁶)) for positive letters. Which is right?
- ab²/(3c³)
- ab⁴/(3c³)
- ab²/(9c³)
6.
Milo says √(x² + 9) = x + 3 for x > 0. Agree or disagree?
- Agree: √(x²) is x and √9 is 3
- Disagree: try x = 4
- Agree: it works for x = 0
7.
Noah says √(x² + 16) simplifies to x + 4 for x > 0. Agree or disagree?
- Agree: 16 is a perfect square
- Agree: root each part of the sum
- Disagree: try x = 3
8.
Pia says √(x³) = x³ for x > 1. Agree or disagree?
- Agree: roots leave powers alone
- Agree: odd powers can't change
- Disagree: it is x√x
9.
Ren's answer is 3x²√2 for x > 0. Which expression did Ren start with?
- √(18x²)
- √(6x⁴)
- √(18x⁴)
10.
Tala's answer is 2y√(5y) for y > 0. Which expression did Tala start with?
- √(20y³)
- √(10y³)
- √(20y²)

Simplify square roots with letters or a fraction inside. Every version has 10 questions, and the answer key prints on the second page.

I can simplify √(x⁸) = x⁴ by halving an even power: one x out for each pair.
I can simplify roots with numbers and letters together, like √(48x⁶) = 4x³√3.
I can take the root of a fraction, top and bottom, and leave what has no pair inside.
I can check by squaring and spot the false step √(x² + 9) = x + 3.

Standard: N-RN.A.2 (partial)

square root: The number that times itself gives what is inside

pair: Two equal factors side by side, like x · x

simplified: No pair is left inside the root

positive letters: Every letter stands for a number above 0 here

fraction root: √(a/b) = √a ÷ √b

Your child took the square root of the exponent. √(x¹⁶) is x⁸, because x⁸ · x⁸ = x¹⁶.

Your child left the fraction as it was. Take the square root of the top and of the bottom.

Your child put the whole square in front, for example 25 for √75.

Ask: how many pairs of x are there?

Ask: what number times itself makes 25?

What is the most common mistake with simplify square roots with letters or a fraction inside?

Your child took the square root of the exponent. √(x¹⁶) is x⁸, because x⁸ · x⁸ = x¹⁶.

How can I help my child with simplify square roots with letters or a fraction inside?

Ask: how many pairs of x are there?

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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