nth roots, and simplify, multiply, add and rationalize radicals

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Bo's robot screen shows ⁶√729. The strip shows its 6 equal factors, ? × ? × ? × ? × ? × ? = 729. What is ⁶√729?

   3
2. 2.

   Esme's math book shows ∜10000. The strip shows its 4 equal factors, ? × ? × ? × ? = 10000. What is ∜10000?

   10
3. 3.

   Kira writes ⁵√(x²) as one power of x on the class board, for x ≥ 0. The strip shows x² split into 5 equal factors. What is the power?

   2/5
4. 4.

   Luz's robot reads only powers, so ∛(x⁴) must become x to one power, for x ≥ 0. The strip shows x⁴ split into 3 equal factors. What is the power?

   4/3
5. 5.

   Noah rewrites x^(2/3) with a root sign, for x ≥ 0. Which root form equals x^(2/3)?

   • √(x³)
   • x² ÷ 3
   • ∛(x²)
   • ∛x
6. 6.

   Pia copies x^(5/4) onto a math club card as a root, for x ≥ 0. Which root form equals x^(5/4)?

   • ⁵√(x⁴)
   • ∜(x⁵)
   • ∜x
   • x⁵ ÷ 4
7. 7.

   Ren sorts math club cards into real and not real. One card says ∜(-81). Which is ∜(-81)?

   • -3, as if the root were odd
   • 3
   • not a real number
8. 8.

   Tala's robot screen shows ⁵√(-32). Which is ⁵√(-32)?

   • 2
   • -2
   • not a real number
9. 9.

   Zee's math book asks about ⁶√(-64). Which is ⁶√(-64)?

   • 2
   • not a real number
   • -2
10. 10.

    Ari writes ⁵√(-243) on the class board. Which is ⁵√(-243)?

    • 3
    • not a real number
    • -3