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 - Building Confidence

NameDate

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

Ari solves x² = 196 on a puzzle card (the card insists it is easy). Two numbers work, one on each side of 0. What is the smaller solution?
Bo solves x² = 121 with a freshly sharpened pencil. Two numbers work, one on each side of 0. What is the smaller solution?
Esme's robot solves x² = 361 and beeps twice, once for each answer. Two numbers work, one on each side of 0. What is the smaller solution?
In math club, Jun solves x² = 256. Two numbers work, one on each side of 0. What is the smaller solution?
Kira lays 4 equal square tiles that cover 324 square inches in all. So 4x² = 324, where x is a side. Divide both sides by 4 first. What is the side length x?
Luz sews 9 equal square patches that cover 576 square inches in all. So 9x² = 576, where x is a side. Divide both sides by 9 first. What is the side length x?
Noah's greenhouse door has 25 equal square glass panes covering 900 square inches. So 25x² = 900, where x is a side. Divide both sides by 25 first. What is the side length x?
8.
Pia's puzzle card says x² = -36. How many real solutions does it have?
- Infinitely many solutions
- Two real solutions
- No real solution
- One real solution
9.
Ren writes 4x² = -100 in orange crayon. How many real solutions does it have?
- One real solution
- Infinitely many solutions
- Two real solutions
- No real solution
10.
Zee's robot is stuck on -3x² = 0. How many real solutions does it have?
- Two real solutions
- No real solution
- Infinitely many solutions
- One real solution

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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