Add, subtract and multiply square roots and cube roots

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Kira's worksheet shows 3√5 + 4√5. The strip shows the copies of √5. What is the sum? Write it like 2√11.

   7√5
2. 2.

   Luz's robot adds 2√7 + 6√7 (and beeps twice to show it is thinking). The strip shows the copies of √7. What is the sum? Write it like 2√11.

   8√7
3. 3.

   In math club, Milo adds 5√3 + 3√3. The strip shows the copies of √3. What is the sum? Write it like 2√11.

   8√3
4. 4.

   Pia's rug is √3 m wide and √27 m long, so its area is √3 × √27 square meters. It equals √(3 × 27). What whole number is √3 × √27?

   9
5. 5.

   Tala's robot multiplies √6 × √24 under one root. It equals √(6 × 24). What whole number is √6 × √24?

   12
6. 6.

   In math club, Zee multiplies √7 × √28. It equals √(7 × 28). What whole number is √7 × √28?

   14
7. 7.

   Ari sorts four expressions on a worksheet. Which one can be written as a single root term?

   • 4√3 + 2
   • 4√3 + 2√3
   • 4 + 2√3
   • 4√3 + 2√5
8. 8.

   Bo's robot can only join like pieces. Which one can be written as a single root term?

   • 7√2 − 3√7
   • 7√2 − 3√2
   • 7 − 3√2
   • 7√2 − 3
9. 9.

   In math club, Esme looks at four expressions. Which one can be written as a single root term?

   • 5√6 + √5
   • 5√6 + 6
   • 5 + √6
   • 5√6 + √6
10. 10.

    Jun's padlock opens for the one that joins (the others just jiggle). Which one can be written as a single root term?

    • 9√5 − 2√3
    • 9√5 − 2
    • 9√5 − 2√5
    • 9 − 2√5