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

NameDate

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

Bo solves x² + 40 = 121 before lunch. What is the positive solution?
Esme's robot solves 4x² - 56 = 200, one careful step at a time. What is the positive solution?
Kira solves (x - 5)² = 81 while waiting for wind. What is the larger solution?
Luz's puzzle card says (x + 4)² = 121. What is the smaller solution?
Milo solves (x - 7)² = 36 for a gold-star challenge. What is the smaller solution?
Noah's robot solves (x + 6)² = 169 (and hums while it works). What is the larger solution?
7.
Pia meets x² + 20 = 4 in a puzzle book. How many real solutions does it have?
- Two real solutions
- No real solution
- Infinitely many solutions
- One real solution
8.
Ren writes (x - 4)² = -9 in pencil. How many real solutions does it have?
- Two real solutions
- Infinitely many solutions
- One real solution
- No real solution
9.
Tala's math book shows 3x² + 11 = 11. How many real solutions does it have?
- Infinitely many solutions
- One real solution
- No real solution
- Two real solutions
10.
Zee's robot reads 2(x + 1)² = 0. How many real solutions does it have?
- Infinitely many solutions
- One real solution
- No real solution
- Two real solutions

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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