Grade 8 · Math

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

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Square roots, cube roots and equations like x² = 49

Grade 8 Math Worksheet

NameDate

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

In math club, Ari finds √(9/16). What is √(9/16)?
In math club, Bo finds √0.36. What is √0.36?
In math club, Jun finds ∛-27. What is ∛-27?
In math club, Kira finds ∛-125. What is ∛-125?
In math club, Luz finds ∛(1/8). What is ∛(1/8)?
In math club, Milo solves x² = 1/4. What are both values of x? Type them as a list.
In math club, Noah solves x² = 0.49. What are both values of x? Type them as a list.
In math club, Pia solves x² = 36/49. What are both values of x? Type them as a list.
In math club, Ren solves x³ = -64. What value or values of x work? Type them as a list.
In math club, Milo finds √(16/49). What is √(16/49)?

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.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records