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).

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

2) $ -3^2 $
Note: This means $ -(3^2) $, not $ (-3)^2 $.
So: $ - (3 \times 3) = -9 $

> ⚠️ Important: The negative sign is *not* inside parentheses, so it applies after squaring.

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

4) $ (-5)^2 $
Here, the negative is included in the base:
$ (-5)^2 = (-5) \times (-5) = 25 $

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

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

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

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

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B. Find the answer. If not possible, write IMPOSSIBLE

These are square roots.

11) $ \sqrt{16} = 4 $ → Given

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

13) $ \sqrt{-100} $
Square root of a negative number is not real.
→ IMPOSSIBLE

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

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

16) $ \sqrt{1600} $
$ \sqrt{1600} = 40 $ (since $ 40 \times 40 = 1600 $)

17) $ \sqrt{8100} $
$ \sqrt{8100} = 90 $ (since $ 90 \times 90 = 8100 $)

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

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

20) $ \sqrt{-64} $
Negative number under square root → IMPOSSIBLE

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C. Find the answer. If not possible, write IMPOSSIBLE

These are cube roots (third roots). Cube roots can be negative.

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

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

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

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

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

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

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

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

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

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

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✔ Final Answers:

#### A.
1) $ 2^4 = 16 $
2) $ -3^2 = -9 $
3) $ 4^3 = 64 $
4) $ (-5)^2 = 25 $
5) $ 10^3 = 1000 $
6) $ 12^2 = 144 $
7) $ (-8)^3 = -512 $
8) $ 7^2 = 49 $

#### B.
11) $ \sqrt{16} = 4 $
12) $ \sqrt{25} = 5 $
13) $ \sqrt{-100} = \text{IMPOSSIBLE} $
14) $ \sqrt{81} = 9 $
15) $ \sqrt{144} = 12 $
16) $ \sqrt{1600} = 40 $
17) $ \sqrt{8100} = 90 $
18) $ \sqrt{49} = 7 $
19) $ \sqrt{121} = 11 $
20) $ \sqrt{-64} = \text{IMPOSSIBLE} $

#### C.
21) $ \sqrt[3]{8} = 2 $
22) $ \sqrt[3]{27} = 3 $
23) $ \sqrt[3]{125} = 5 $
24) $ \sqrt[3]{1000} = 10 $
25) $ \sqrt[3]{-512} = -8 $
26) $ \sqrt[3]{-125} = -5 $
27) $ \sqrt[3]{64} = 4 $
28) $ \sqrt[3]{343} = 7 $
29) $ \sqrt[3]{729} = 9 $
30) $ \sqrt[3]{216} = 6 $

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✔ All problems solved! Let me know if you'd like this formatted for printing or as a worksheet.