Square roots, cube roots and equations like x² = 49

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. 1.

   In math club, Ari solves x² + 7 = 151. What are both values of x? Type them as a list.

   12, -12
2. 2.

   In math club, Bo solves 2x² = 128. What are both values of x? Type them as a list.

   8, -8
3. 3.

   In math club, Esme solves x² − 10 = 15. What are both values of x? Type them as a list.

   5, -5
4. 4.

   In math club, Jun solves x³ + 5 = -3. What value or values of x work? Type them as a list.

   -2
5. 5.

   In math club, Kira solves 3x³ = 81. What value or values of x work? Type them as a list.

   3
6. 6.

   In math club, Luz solves x³ − 20 = 105. What value or values of x work? Type them as a list.

   5
7. 7.

   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?

   √50
8. 8.

   Pia's square quilt covers 30 square feet. What is the exact length of each side, in feet, written with a root sign?

   √30
9. 9.

   Ren's worksheet asks for 2√49 + ∛64. Work out the roots first. What is 2√49 + ∛64?

   18
10. 10.

    Zee's worksheet asks for (∛125)² − √36. Work out the roots first. What is (∛125)² − √36?

    19