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

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Bo clears the root from the bottom of 4/(3 − √5) for a math club card. Which is 4/(3 − √5) with a whole-number bottom?

   • (6 + 2√5)/7
   • 3 − √5
   • 3 + √5
   • 1
2. 2.

   Esme's robot shows 9/(√7 + 2) and needs a whole-number bottom. Which is 9/(√7 + 2) with a whole-number bottom?

   • 3
   • 3√7 + 6
   • (9√7 − 18)/11
   • 3√7 − 6
3. 3.

   Jun's math book asks to rationalize 2/(√5 + √3). Which is 2/(√5 + √3) with a whole-number bottom?

   • √5 + √3
   • √5 − √3
   • (√5 − √3)/4
   • 1
4. 4.

   Kira simplifies ∛(54x⁷) for x ≥ 0 on a math club card. Which is ∛(54x⁷) fully simplified?

   • 27x⁶∛(2x)
   • 3x²∛2
   • 3x³∛(6x)
   • 3x²∛(2x)
5. 5.

   Milo's math book shows √(75x⁵), for x ≥ 0. Which is √(75x⁵) fully simplified?

   • 5x²√(3x)
   • 5x²√3
   • 25x⁴√(3x)
6. 6.

   Noah divides ∛(81x⁵) ÷ ∛(3x²) for x > 0 on the class board. What is the quotient as one term?

   3x
7. 7.

   Pia's robot divides ∜(48x⁷) ÷ ∜(3x³) for x > 0. What is the quotient as one term?

   2x
8. 8.

   Tala simplifies (16x⁸)^(3/4) for x ≥ 0 on a math club card. What is (16x⁸)^(3/4) as one term?

   8x^6
9. 9.

   Zee's math book shows (27x⁶)^(2/3), for x ≥ 0. What is (27x⁶)^(2/3) as one term?

   9x^4
10. 10.

    Ari's robot simplifies (32x¹⁵)^(2/5) for x ≥ 0. What is (32x¹⁵)^(2/5) as one term?

    4x^6