Square Root and Cube Root Practice | Interactive Worksheet ... - Free Printable

Problem Description:

The task is to find the square roots and cube roots of various numbers listed in the worksheet. The goal is to compute each value accurately.

Solution Approach:

1. Square Root: For a number \( x \), the square root is a value \( y \) such that \( y^2 = x \).
2. Cube Root: For a number \( x \), the cube root is a value \( z \) such that \( z^3 = x \).

We will calculate each value step by step.

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Step-by-Step Calculations:

#### Square Roots:
1. \( \sqrt{81} \):
- \( 9^2 = 81 \)
- Answer: \( 9 \)

2. \( \sqrt{64} \):
- \( 8^2 = 64 \)
- Answer: \( 8 \)

3. \( \sqrt{16} \):
- \( 4^2 = 16 \)
- Answer: \( 4 \)

4. \( \sqrt{16} \):
- \( 4^2 = 16 \)
- Answer: \( 4 \)

5. \( \sqrt{49} \):
- \( 7^2 = 49 \)
- Answer: \( 7 \)

6. \( \sqrt{225} \):
- \( 15^2 = 225 \)
- Answer: \( 15 \)

7. \( \sqrt{27} \):
- \( \sqrt{27} \approx 5.196 \) (since \( 5.196^2 \approx 27 \))
- Answer: \( \approx 5.196 \)

8. \( \sqrt{100} \):
- \( 10^2 = 100 \)
- Answer: \( 10 \)

9. \( \sqrt{169} \):
- \( 13^2 = 169 \)
- Answer: \( 13 \)

10. \( \sqrt{256} \):
- \( 16^2 = 256 \)
- Answer: \( 16 \)

11. \( \sqrt{1,000} \):
- \( \sqrt{1,000} \approx 31.623 \) (since \( 31.623^2 \approx 1,000 \))
- Answer: \( \approx 31.623 \)

12. \( \sqrt{512} \):
- \( \sqrt{512} \approx 22.627 \) (since \( 22.627^2 \approx 512 \))
- Answer: \( \approx 22.627 \)

13. \( \sqrt{324} \):
- \( 18^2 = 324 \)
- Answer: \( 18 \)

14. \( \sqrt{125} \):
- \( \sqrt{125} \approx 11.180 \) (since \( 11.180^2 \approx 125 \))
- Answer: \( \approx 11.180 \)

15. \( \sqrt{1,331} \):
- \( \sqrt{1,331} \approx 36.483 \) (since \( 36.483^2 \approx 1,331 \))
- Answer: \( \approx 36.483 \)

16. \( \sqrt{1,728} \):
- \( \sqrt{1,728} \approx 41.570 \) (since \( 41.570^2 \approx 1,728 \))
- Answer: \( \approx 41.570 \)

17. \( \sqrt{196} \):
- \( 14^2 = 196 \)
- Answer: \( 14 \)

18. \( \sqrt{361} \):
- \( 19^2 = 361 \)
- Answer: \( 19 \)

#### Cube Roots:
19. \( \sqrt[3]{1,000} \):
- \( 10^3 = 1,000 \)
- Answer: \( 10 \)

20. \( \sqrt[3]{361} \):
- \( \sqrt[3]{361} \approx 7.120 \) (since \( 7.120^3 \approx 361 \))
- Answer: \( \approx 7.120 \)

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Final Answers:

\[
\begin{array}{cccc}
1. & \sqrt{81} = 9 & 2. & \sqrt{64} = 8 \\
3. & \sqrt{16} = 4 & 4. & \sqrt{16} = 4 \\
5. & \sqrt{49} = 7 & 6. & \sqrt{225} = 15 \\
7. & \sqrt{27} \approx 5.196 & 8. & \sqrt{100} = 10 \\
9. & \sqrt{169} = 13 & 10. & \sqrt{256} = 16 \\
11. & \sqrt{1,000} \approx 31.623 & 12. & \sqrt{512} \approx 22.627 \\
13. & \sqrt{324} = 18 & 14. & \sqrt{125} \approx 11.180 \\
15. & \sqrt{1,331} \approx 36.483 & 16. & \sqrt{1,728} \approx 41.570 \\
17. & \sqrt{196} = 14 & 18. & \sqrt{361} = 19 \\
19. & \sqrt[3]{1,000} = 10 & 20. & \sqrt[3]{361} \approx 7.120 \\
\end{array}
\]

Boxed Final Answer:

\[
\boxed{
\begin{array}{cccc}
1. & 9 & 2. & 8 \\
3. & 4 & 4. & 4 \\
5. & 7 & 6. & 15 \\
7. & \approx 5.196 & 8. & 10 \\
9. & 13 & 10. & 16 \\
11. & \approx 31.623 & 12. & \approx 22.627 \\
13. & 18 & 14. & \approx 11.180 \\
15. & \approx 36.483 & 16. & \approx 41.570 \\
17. & 14 & 18. & 19 \\
19. & 10 & 20. & \approx 7.120 \\
\end{array}
}
\]