Simplify square roots with letters or a fraction inside

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Ari's robot screen shows √(x^16) for x > 0 (the robot only counts in pairs). It simplifies to x to a whole power. What is that power?

   8
2. 2.

   Bo's puzzle card shows √(x^36) for x > 0. It simplifies to x to a whole power. What is that power?

   18
3. 3.

   In math club, Esme writes √(x^64) for x > 0 on the board. It simplifies to x to a whole power. What is that power?

   32
5. 4.

   Using the card, why is √(x⁶) equal to x³, Jun?

   • Three pairs give three x's out
   • x⁶ has three factors
   • 6 ÷ 3 = 3
6. 5.

   Using the card, why does √y stay in y²√y, Kira?

   Use the picture in question 4.

   • y² is too big to pull
   • y is too small to come out
   • One y has no partner
7. 6.

   Milo's pizza slice covers 25/49 of a square box lid. What is √(25/49)?

   • 5/7
   • 25/7
   • 5/49
8. 7.

   Noah simplifies √(1/36) on a quiz card. Which is right?

   • 6
   • 1/18
   • 1/6
9. 8.

   Pia simplifies √(x²/9) for x > 0. Which is right?

   • x²/3
   • x/9
   • x/3
10. 9.

    In Ren's strip, a pair of x's sits under a square root. What comes out?

    • Two x's
    • One x
    • x²
11. 10.

    On Zee's sheet, letters stand for positive numbers. What is √(x²)?

    • x/2
    • 2x
    • x