Add, subtract and multiply square roots and cube roots

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Luz's robot multiplies out √3(√12 + 5). Which is the product, fully simplified?

   • √15 + 5√3
   • 36 + 5√3
   • 6 + 5√3
   • 11
2. 2.

   In math club, Milo multiplies out √5(√20 − 2). Which is the product, fully simplified?

   • 10 − 2√5
   • 8
   • √25 − 2√5
   • 100 − 2√5
3. 3.

   Noah's padlock tag shows √6(√6 + 4) (it is a very fancy padlock). Which is the product, fully simplified?

   • 36 + 4√6
   • 10
   • √12 + 4√6
   • 6 + 4√6
4. 4.

   Pia stacks two cube-shaped blocks with edges ∛24 cm and ∛81 cm. How tall is the stack, as a whole number times ∛3? What is that whole number?

   5
5. 5.

   Ren's robot works out ∛250 − ∛16. The answer is a whole number times ∛2. What is that whole number?

   3
6. 6.

   Tala stacks two cube-shaped boxes with edges ∛16 inches and ∛128 inches (a wobbly tower). How tall is the stack, as a whole number times ∛2? What is that whole number?

   6
7. 7.

   Zee's worksheet shows ∛375 − ∛81. The answer is a whole number times ∛3. What is that whole number?

   2
8. 8.

   Each side of Ari's square tile is √18 cm. The distance around it is a whole number times √2 cm. What is that whole number?

   12
9. 9.

   Each side of Bo's square card is √50 cm (a card for very exact birthday wishes). The distance around it is a whole number times √2 cm. What is that whole number?

   20
10. 10.

    Each side of Esme's square window pane is √27 cm. The distance around it is a whole number times √3 cm. What is that whole number?

    12