Simplify square roots with letters or a fraction inside

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Ari's robot simplifies √(75x^4) for x > 0 (it hums while it works). Fully simplified, what whole number is in front?

   5
2. 2.

   Bo simplifies √(147x^6) for x > 0 in math club. Fully simplified, what whole number is in front?

   7
3. 3.

   Esme's puzzle card shows √(128x^2) for x > 0. Fully simplified, what whole number is in front?

   8
4. 4.

   Jun simplifies √(x⁶/(4y²)) for positive x and y. Which is right?

   • x³/(4y)
   • x³/(2y)
   • x⁶/(2y)
5. 5.

   Kira simplifies √(12x³/25) for x > 0. Which is fully simplified?

   • 2x√(3x)/5
   • 2x√(3x)/25
   • 4x√(3x)/5
6. 6.

   Luz simplifies √(a²b⁴/(9c⁶)) for positive letters. Which is right?

   • ab²/(9c³)
   • ab²/(3c³)
   • ab⁴/(3c³)
7. 7.

   Noah says √(x² + 16) simplifies to x + 4 for x > 0. Agree or disagree?

   • Disagree: try x = 3
   • Agree: root each part of the sum
   • Agree: 16 is a perfect square
8. 8.

   Pia says √(x³) = x³ for x > 1. Agree or disagree?

   • Agree: odd powers can't change
   • Agree: roots leave powers alone
   • Disagree: it is x√x
9. 9.

   Tala's answer is 2y√(5y) for y > 0. Which expression did Tala start with?

   • √(20y³)
   • √(10y³)
   • √(20y²)
10. 10.

    Zee's answer is x/4 for x > 0. Which expression did Zee start with?

    • √(x/16)
    • √(x²/4)
    • √(x²/16)