Simplify square roots with letters or a fraction inside

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Ari works out √(64/81), a little like sharing a square cookie fairly. What is it as a fraction in simplest form?

   8/9
2. 2.

   Bo works out √(49/100), a little like sharing a square quilt fairly. What is it as a fraction in simplest form?

   7/10
3. 3.

   Esme works out √(121/144), a little like sharing a square rug fairly. What is it as a fraction in simplest form?

   11/12
4. 4.

   Jun simplifies √(48x⁶) for x > 0. Which is fully simplified?

   • 4x³√3
   • 4x⁶√3
   • 16x³√3
5. 5.

   Kira simplifies √(x²y⁶) for positive x and y. Which is right?

   • xy³
   • xy⁶
   • x²y³
6. 6.

   Milo simplifies √(7/9). Which is right?

   • 7/3
   • √7/9
   • √7/3
7. 7.

   Pia simplifies √(x⁴/25) for x > 0. Which is right?

   • x²/5
   • x⁴/5
   • x²/25
8. 8.

   Ren says √(x⁸) = x⁴ for x > 0. Which check proves it?

   • x⁸ ÷ 2 = x⁴
   • x⁴ + x⁴ = x⁸
   • (x⁴)² = x⁸
9. 9.

   Tala writes √(9x) = 3x for x > 0. What does squaring 3x show?

   • 9x², so it's wrong
   • 9x, so it is right as written
   • 6x, so it's wrong
10. 10.

    Zee gets √(4/25) = 2/5. Which square checks it?

    • (2/5)² = 4/5
    • 2/5 × 2 = 4/25
    • (2/5)² = 4/25