Simplify a square root or cube root

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Ari's puzzle card shows ∛(-54), the cube root of a negative number. Ari simplifies it fully, as a whole number times a cube root. What whole number is in front?

   -3
2. 2.

   Bo's robot screen shows ∛(-250) (the robot is not worried about the minus sign). Bo simplifies it fully, as a whole number times a cube root. What whole number is in front?

   -5
3. 3.

   Jun's padlock tag shows ∛(-16). Jun simplifies it fully, as a whole number times a cube root. What whole number is in front?

   -2
4. 4.

   Kira simplifies √(x^9) for x ≥ 0 by pulling each pair x × x out of the root. The answer is x to a power times √x. What is that power?

   4
5. 5.

   In math club, Luz simplifies √(x^7) for x ≥ 0, one pair of x at a time. The answer is x to a power times √x. What is that power?

   3
6. 6.

   Milo's robot simplifies √(x^11) for x ≥ 0 (it loves pairs, like socks). The answer is x to a power times √x. What is that power?

   5
7. 7.

   Noah's math book shows √(x^5) for x ≥ 0. The answer is x to a power times √x. What is that power?

   2
8. 8.

   Pia wants 7√2 written as one root, √n, with nothing in front. What is n?

   98
9. 9.

   Ren's robot only reads single roots, so 4√6 must become √n. What is n?

   96
10. 10.

    Zee's padlock opens with the number n in √n = 2√13. What is n?

    52