Grade 8 · Math

8th grade Square roots, cube roots and equations like x² = 49 worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Square roots, cube roots and equations like x² = 49

Grade 8 Math Worksheet - Challenge Me

NameDate

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

In math club, Bo solves 2x² = 128. What are both values of x? Type them as a list.
In math club, Esme solves x² − 10 = 15. What are both values of x? Type them as a list.
In math club, Jun solves x³ + 5 = -3. What value or values of x work? Type them as a list.
In math club, Kira solves 3x³ = 81. What value or values of x work? Type them as a list.
In math club, Milo solves x² = 50, where x is positive. 50 is not a perfect square. What is x, written exactly with a root sign?
Noah cuts a square of paper with an area of 20 square inches. What is the exact length of each side, in inches, written with a root sign?
Pia's square quilt covers 30 square feet. What is the exact length of each side, in feet, written with a root sign?
Tala's worksheet asks for √81 − 2∛64. Work out the roots first. What is √81 − 2∛64?
Zee's worksheet asks for (∛125)² − √36. Work out the roots first. What is (∛125)² − √36?
Ari's worksheet asks for √(9/25) + ∛-8. Work out the roots first. What is √(9/25) + ∛-8?

Square roots, cube roots and equations like x² = 49. Every version has 10 questions, and the answer key prints on the second page.

I can find square roots and cube roots, including of fractions, decimals and negative numbers (∛−27 = −3).
I can solve x² = p (two answers) and x³ = q (one answer), also after undoing a first step.
I can write an exact root such as √50 when the number is not a perfect square, and work out expressions such as 2√49 + ∛64.

Standard: 8.EE.A.2

square root √: The number that times itself makes it: √64 = 8.

cube root ∛: The number that three times makes it: ∛64 = 4.

perfect square / cube: A whole number times itself (twice / three times).

exact root: A root left with its sign, like √50, when it is not whole.

solution: A value of x that makes the equation true.

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

Your child divided by 3 instead of finding a cube root.

Your child found a square root where a cube root was asked.

Ask: which number times itself makes it?

Ask: which number, used three times, multiplies to make it?

Ask: does the little 3 mean two equal factors or three?

What is the most common mistake with square roots, cube roots and equations like x² = 49?

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

How can I help my child with square roots, cube roots and equations like x² = 49?

Ask: which number times itself makes it?

Are these 8th 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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