MIA · Mixed set · Unit 6

1. 1.

   Evaluate √64.

   Answer. 8

   8² = 64.

2. 2.

   Write 38 as a decimal.

   Answer. 0.375

   3 ÷ 8 = 0.375.

3. 3.

   Between which two consecutive integers does √2 lie?

   Answer. 1 and 2

   1² = 1 and 2² = 4, and 1 < 2 < 4.

4. 4.

   A right triangle has legs 7 and 24. What is the hypotenuse?

   Answer. 25

   7² + 24² = 625 = 25².

5. 5.

   A rectangle is 7 by 24. How long is a diagonal? Then Malik needs 5 of that amount. What is the total they need?

   Answer. 125

   Diagonal² = 7² + 24² = 25², so the diagonal is 25. Then multiply by 5: 125.

6. 6.

   A sphere has radius 3 cm. Volume in terms of π? Write a complete answer — Priya will compare with a partner.

   Answer. 36π cubic cm

   V = (43)πr³ = (43)π(27) = 36π.

7. 7.

   Evaluate √25. Then Nora needs 3 of that amount. What is the total they need?

   Answer. 15

   5² = 25. Then multiply by 3: 15.

8. 8.

   Write 1.75 as a fraction in simplest form. Then Malik needs 3 of that amount. What is the total they need?

   Answer. 514

   1.75 = 74 = 134. Then multiply by 3: 514.

9. 9.

   Between which two consecutive integers does √3 lie? Then Malik needs 2 of that amount. What is the total they need?

   Answer. 2 and 2

   1² = 1 and 2² = 4, and 1 < 3 < 4. Then multiply by 2: 2 and 2.

10. 10.

    A right triangle has legs 12 and 16. What is the hypotenuse? Then Ava needs 5 of that amount. What is the total they need?

    Answer. 100

    12² + 16² = 400 = 20². Then multiply by 5: 100.

11. 11.

    Think

    Sam tried this problem:
    A rectangle is 9 by 40. How long is a diagonal?
    Sam wrote 82. That is not correct. What is the right answer?

    Answer. 41

    Sam’s answer 82 is off. Diagonal² = 9² + 40² = 41², so the diagonal is 41.

12. 12.

    Think

    Ava tried this problem:
    A sphere has radius 6 cm. Volume in terms of π?
    Ava wrote 287π cubic cm. That is not correct. What is the right answer?

    Answer. 288π cubic cm

    Ava’s answer 287π cubic cm is off. V = (43)πr³ = (43)π(216) = 288π.

Original extra practice. Keys are computed from the items, not guessed.