Square and cube roots worksheet - Free Printable

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

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A. Find the answer, show your working

We are dealing with exponents (powers).

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1) $ 2^4 = 2 \times 2 \times 2 \times 2 = 16 $

2) $ -3^2 $
⚠️ Note: The exponent applies only to 3, not the negative sign unless in parentheses.
So: $ -3^2 = -(3^2) = -(9) = -9 $

3) $ 4^3 = 4 \times 4 \times 4 = 64 $

4) $ (-5)^2 = (-5) \times (-5) = 25 $

5) $ 10^3 = 10 \times 10 \times 10 = 1000 $

6) $ 12^2 = 12 \times 12 = 144 $

7) $ (-8)^3 = (-8) \times (-8) \times (-8) = 64 \times (-8) = -512 $

8) $ 7^2 = 7 \times 7 = 49 $

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✔ A Answers:
1) 16
2) -9
3) 64
4) 25
5) 1000
6) 144
7) -512
8) 49

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B. Find the answer. If not possible write IMPOSSIBLE

These are square roots.

Remember:
- Square root of a positive number is real.
- Square root of a negative number is not real → write IMPOSSIBLE (assuming we're working with real numbers).
- √(a²) = |a|, so positive root.

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11) $ \sqrt{16} = 4 $ (since $ 4^2 = 16 $)

12) $ \sqrt{25} = 5 $ (since $ 5^2 = 25 $)

13) $ \sqrt{-100} $ → Negative number → IMPOSSIBLE

14) $ \sqrt{81} = 9 $ (since $ 9^2 = 81 $)

15) $ \sqrt{144} = 12 $ (since $ 12^2 = 144 $)

16) $ \sqrt{1600} $ → Let's simplify:
$ \sqrt{1600} = \sqrt{16 \times 100} = \sqrt{16} \times \sqrt{100} = 4 \times 10 = 40 $

17) $ \sqrt{8100} $ → $ \sqrt{81 \times 100} = \sqrt{81} \times \sqrt{100} = 9 \times 10 = 90 $

18) $ \sqrt{49} = 7 $ (since $ 7^2 = 49 $)

19) $ \sqrt{121} = 11 $ (since $ 11^2 = 121 $)

20) $ \sqrt{-64} $ → Negative → IMPOSSIBLE

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✔ B Answers:
11) 4
12) 5
13) IMPOSSIBLE
14) 9
15) 12
16) 40
17) 90
18) 7
19) 11
20) IMPOSSIBLE

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C. Find the answer. If not possible write IMPOSSIBLE

These are cube roots ($ \sqrt[3]{} $)

Cube roots can be taken for negative numbers, because odd roots of negatives are defined.

For example: $ \sqrt[3]{-8} = -2 $, since $ (-2)^3 = -8 $

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21) $ \sqrt[3]{8} = 2 $ (since $ 2^3 = 8 $)

22) $ \sqrt[3]{27} = 3 $ (since $ 3^3 = 27 $)

23) $ \sqrt[3]{125} = 5 $ (since $ 5^3 = 125 $)

24) $ \sqrt[3]{1000} = 10 $ (since $ 10^3 = 1000 $)

25) $ \sqrt[3]{-512} = -8 $ (since $ (-8)^3 = -512 $)

26) $ \sqrt[3]{-125} = -5 $ (since $ (-5)^3 = -125 $)

27) $ \sqrt[3]{64} = 4 $ (since $ 4^3 = 64 $)

28) $ \sqrt[3]{343} = 7 $ (since $ 7^3 = 343 $)

29) $ \sqrt[3]{729} = 9 $ (since $ 9^3 = 729 $)

30) $ \sqrt[3]{216} = 6 $ (since $ 6^3 = 216 $)

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✔ C Answers:
21) 2
22) 3
23) 5
24) 10
25) -8
26) -5
27) 4
28) 7
29) 9
30) 6

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✔ Final Answers Summary:

#### A:
1) 16
2) -9
3) 64
4) 25
5) 1000
6) 144
7) -512
8) 49

#### B:
11) 4
12) 5
13) IMPOSSIBLE
14) 9
15) 12
16) 40
17) 90
18) 7
19) 11
20) IMPOSSIBLE

#### C:
21) 2
22) 3
23) 5
24) 10
25) -8
26) -5
27) 4
28) 7
29) 9
30) 6

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Let me know if you'd like this formatted as a printable sheet or need explanations for any specific one!