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Exponents and radicals practice

Square and cube equations worksheets

Generate 18 equations with squared, cubed or rooted variables. Set magnitudes from 1 to 20, choose equation types and select the signs of cubic values.

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Solve each equation over the real numbers. Give both roots of a positive square equation; a cube equation has one real root.

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The original equation decides

A value is a solution only if the original expressions are real and the two sides are equal. Squaring both sides can introduce candidates that fail this final check.

A positive square equation has two opposite roots, while a principal square-root expression has one nonnegative value. Keep those two instructions distinct.

The selected range applies to the base or root magnitude, not the powered result. A very narrow range may intentionally repeat facts to keep the full 18-question practice set.

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Learning objective

What this activity builds

Use inverse operations to solve square and cube equations while distinguishing two square roots from a principal-root value.

Worked example

Solve x² = 64 and ∛y = −4.

x = −8 or 8; y = −64.

Both −8 and 8 square to 64. Cubing both sides of the second equation gives y = (−4)³ = −64.

Teaching notes

Make the practice count

  • Write both square-equation solutions as a set.
  • Compare x² = 64 with √x = 8.
  • Use negative cubic values to practice odd-root signs.
  • The cubic-sign setting does not create negative principal square roots.

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Math SheetNameScore/ 18TeacherDateSquare and Cube EquationsSolve square and cube equations over the real numbers.1.x249Domain: real variablesxR2.x3343Domain: real variablesxR3.x3-343Domain: real variablesxR4.x264Domain: real variablesxR5.x3512Domain: real variablesxR6.x3-512Domain: real variablesxR7.x281Domain: real variablesxR8.x3729Domain: real variablesxR9.x3-729Domain: real variablesxR10.x2100Domain: real variablesxR11.x31000Domain: real variablesxR12.x3-1000Domain: real variablesxR13.x2121Domain: real variablesxR14.x31331Domain: real variablesxRmath-sheet.comPage 1 / 2
Math SheetNameScore/ 18TeacherDateSquare and Cube EquationsSolve square and cube equations over the real numbers.15.x3-1331Domain: real variablesxR16.x2144Domain: real variablesxR17.x31728Domain: real variablesxR18.x3-1728Domain: real variablesxRmath-sheet.comPage 2 / 2

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