Using Square and Cube Roots Worksheet Download - Free Printable

Let's solve each part of the problem step by step.

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Part 1: Evaluate the cubes

We need to compute $ a^3 $, which means $ a \times a \times a $.

1. $ 4^3 = 4 \times 4 \times 4 = 16 \times 4 = \boxed{64} $

2. $ 3^3 = 3 \times 3 \times 3 = 9 \times 3 = \boxed{27} $

3. $ 10^3 = 10 \times 10 \times 10 = 100 \times 10 = \boxed{1000} $

4. $ 6^3 = 6 \times 6 \times 6 = 36 \times 6 = \boxed{216} $

5. $ (-2)^3 = (-2) \times (-2) \times (-2) = 4 \times (-2) = \boxed{-8} $

6. $ 8^3 = 8 \times 8 \times 8 = 64 \times 8 = \boxed{512} $

7. $ (-5)^3 = (-5) \times (-5) \times (-5) = 25 \times (-5) = \boxed{-125} $

8. $ 9^3 = 9 \times 9 \times 9 = 81 \times 9 = \boxed{729} $

9. $ 7^3 = 7 \times 7 \times 7 = 49 \times 7 = \boxed{343} $

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Part 2: Evaluate the cube roots

We are finding $ \sqrt[3]{x} $, which is the number that, when cubed, gives $ x $.

1. $ \sqrt[3]{27} = ? $
Since $ 3^3 = 27 $, then $ \sqrt[3]{27} = \boxed{3} $

2. $ \sqrt[3]{125} = ? $
Since $ 5^3 = 125 $, then $ \sqrt[3]{125} = \boxed{5} $

3. $ \sqrt[3]{-8} = ? $
Since $ (-2)^3 = -8 $, then $ \sqrt[3]{-8} = \boxed{-2} $

4. $ \sqrt[3]{216} = ? $
Since $ 6^3 = 216 $, then $ \sqrt[3]{216} = \boxed{6} $

5. $ \sqrt[3]{-64} = ? $
Since $ (-4)^3 = -64 $, then $ \sqrt[3]{-64} = \boxed{-4} $

6. $ \sqrt[3]{1000} = ? $
Since $ 10^3 = 1000 $, then $ \sqrt[3]{1000} = \boxed{10} $

7. $ \sqrt[3]{64} = ? $
Since $ 4^3 = 64 $, then $ \sqrt[3]{64} = \boxed{4} $

8. $ \sqrt[3]{-1} = ? $
Since $ (-1)^3 = -1 $, then $ \sqrt[3]{-1} = \boxed{-1} $

9. $ \sqrt[3]{512} = ? $
Since $ 8^3 = 512 $, then $ \sqrt[3]{512} = \boxed{8} $

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✔ Final Answers:

#### Cubes:
- $ 4^3 = 64 $
- $ 3^3 = 27 $
- $ 10^3 = 1000 $
- $ 6^3 = 216 $
- $ (-2)^3 = -8 $
- $ 8^3 = 512 $
- $ (-5)^3 = -125 $
- $ 9^3 = 729 $
- $ 7^3 = 343 $

#### Cube Roots:
- $ \sqrt[3]{27} = 3 $
- $ \sqrt[3]{125} = 5 $
- $ \sqrt[3]{-8} = -2 $
- $ \sqrt[3]{216} = 6 $
- $ \sqrt[3]{-64} = -4 $
- $ \sqrt[3]{1000} = 10 $
- $ \sqrt[3]{64} = 4 $
- $ \sqrt[3]{-1} = -1 $
- $ \sqrt[3]{512} = 8 $

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✔ All answers are now evaluated and explained! Let me know if you'd like this in table format or printable form.