Add, subtract and multiply square roots and cube roots

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Kira's worksheet shows √12 + √27. Simplify each root first. What is the answer as one root term? Write it like 2√11.

   5√3
2. 2.

   Luz measures two rug edges, √50 m and √8 m, and adds them. Simplify each root first. What is the answer as one root term? Write it like 2√11.

   7√2
3. 3.

   Milo's robot works out √75 − √12 (with a very serious face). Simplify each root first. What is the answer as one root term? Write it like 2√11.

   3√3
4. 4.

   In math club, Noah works out √98 − √32. Simplify each root first. What is the answer as one root term? Write it like 2√11.

   3√2
5. 5.

   Pia's worksheet shows 2√3 × 5√6. Fully simplified, the product is a whole number times √2. What is that whole number?

   30
6. 6.

   Ren's robot multiplies 3√2 × 4√10 (and asks for a snack break after). Fully simplified, the product is a whole number times √5. What is that whole number?

   24
7. 7.

   In math club, Tala multiplies 4√5 × 2√15. Fully simplified, the product is a whole number times √3. What is that whole number?

   40
8. 8.

   Zee's padlock code comes from 3√7 × 2√14. Fully simplified, the product is a whole number times √2. What is that whole number?

   42
9. 9.

   In math club, Esme multiplies √3 × √15 on the board. Which is the product fully simplified?

   • √45
   • 3√5
   • √18
   • 9√5
10. 10.

    Jun's window is √2 ft wide and √22 ft tall, so its area is √2 × √22 square feet. Which is the product fully simplified?

    • √24
    • √44
    • 4√11
    • 2√11