Grade 9 · Math · Algebra 1

9th grade Solve ax² = c by taking square roots worksheet

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Solve ax^2 = c by taking square roots

Grade 9 Math Worksheet - Challenge Me

NameDate

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

Bo's robot solves 2x² - 9 = 33 and asks for a tidy answer. What is the positive solution, to the nearest tenth?
Esme solves 5x² + 12 = 47 on graph paper. What is the positive solution, to the nearest tenth?
A square garden has side length x feet. Jun solves 4x² - 7 = 33. What is the positive solution to the nearest tenth?
Kira solves 2(x + 3)² - 5 = 93 on the back of a worksheet. What is the smaller solution?
In math club, Milo solves 3(x + 1)² + 4 = 196. What is the smaller solution?
Noah solves 2(x - 6)² + 1 = 99, eraser ready. What is the smaller solution?
7.
Pia solves x² - 3 = 17 and wants the exact answer, root sign and all. Which gives both exact solutions?
- x = √14 or x = -√14
- x = 10 or x = -10
- x = 2√5 or x = -2√5
- x = 2√5 only
8.
Ren's math book asks for exact solutions of x² + 4 = 22. Which gives both exact solutions?
- x = 9 or x = -9
- x = 3√2 only
- x = √26 or x = -√26
- x = 3√2 or x = -3√2
9.
Tala's robot gives exact answers only. It is solving 3x² = 84. Which gives both exact solutions?
- x = 2√21 or x = -2√21
- x = 2√7 or x = -2√7
- x = 2√7 only
- x = 14 or x = -14
10.
Zee solves 4x² = 96 exactly, no calculator. Which gives both exact solutions?
- x = 4√6 or x = -4√6
- x = 2√6 or x = -2√6
- x = 2√6 only
- x = 12 or x = -12

Solve ax² = c by taking square roots. Every version has 10 questions, and the answer key prints on the second page.

I can find both inputs that square to the same number, one on each side of the mirror line.
I can get x² (or the bracket squared) alone before taking the root.
I can tell when there is one solution or no real solution.

Standard: A-REI.B.4b

square root: A number that, times itself, gives the number under the root.

solution: An input that makes the equation true; a row with output 0.

mirror rows: Two rows with the same output, one on each side of the axis.

no real solution: No real number works, because a square is never negative.

nearest tenth: Rounded to one place after the decimal point.

Your child found the positive square root and missed the negative one.

Your child halved the number instead of finding its square root.

Your child took the square root before dividing by the number in front of x².

Ask: what is (-7) × (-7)?

Ask: which number times itself makes it?

Ask: what is x² on its own?

What is the most common mistake with solve ax² = c by taking square roots?

Your child found the positive square root and missed the negative one.

How can I help my child with solve ax² = c by taking square roots?

Ask: what is (-7) × (-7)?

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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