Square and Cube Root of a number. worksheet - Free Printable

Here are the solutions to the problems on your worksheet. I have worked through each one step-by-step to ensure accuracy.

Part A: Find the answer, show your working.

*These problems ask you to calculate powers (exponents). This means multiplying a number by itself.*

1) $2^2 = 2 \times 2 = 4$ (Already done)

2) $2^4$
Working: $2 \times 2 \times 2 \times 2$
Calculation: $4 \times 2 = 8$, and $8 \times 2 = 16$.
Answer: 16

3) $3^2$
Working: $3 \times 3$
Answer: 9

4) $4^3$
Working: $4 \times 4 \times 4$
Calculation: $4 \times 4 = 16$, and $16 \times 4 = 64$.
Answer: 64

5) $5^2$
Working: $5 \times 5$
Answer: 25

6) $10^3$
Working: $10 \times 10 \times 10$
Calculation: $10 \times 10 = 100$, and $100 \times 10 = 1000$.
Answer: 1000

7) $12^2$
Working: $12 \times 12$
Answer: 144

8) $8^3$
Working: $8 \times 8 \times 8$
Calculation: $8 \times 8 = 64$, and $64 \times 8 = 512$.
Answer: 512

9) $7^2$
Working: $7 \times 7$
Answer: 49

10) $4^3$
Working: $4 \times 4 \times 4$
Calculation: $4 \times 4 = 16$, and $16 \times 4 = 64$.
Answer: 64

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Part B: Find the answer.

*These problems ask for square roots ($\sqrt{}$ or $\sqrt[2]{}$). You need to find a number that, when multiplied by itself, equals the number inside.*

11) $\sqrt[2]{16} = 4$ (Already done, because $4 \times 4 = 16$)

12) $\sqrt[2]{25}$
Thinking: What number times itself is 25? ($5 \times 5 = 25$)
Answer: 5

13) $\sqrt[2]{100}$
Thinking: What number times itself is 100? ($10 \times 10 = 100$)
Answer: 10

14) $\sqrt[2]{81}$
Thinking: What number times itself is 81? ($9 \times 9 = 81$)
Answer: 9

15) $\sqrt[2]{144}$
Thinking: What number times itself is 144? ($12 \times 12 = 144$)
Answer: 12

16) $\sqrt[2]{1600}$
Thinking: We know $\sqrt{16} = 4$ and $\sqrt{100} = 10$. So, $4 \times 10 = 40$. Check: $40 \times 40 = 1600$.
Answer: 40

17) $\sqrt[2]{8100}$
Thinking: We know $\sqrt{81} = 9$ and $\sqrt{100} = 10$. So, $9 \times 10 = 90$. Check: $90 \times 90 = 8100$.
Answer: 90

18) $\sqrt[2]{49}$
Thinking: What number times itself is 49? ($7 \times 7 = 49$)
Answer: 7

19) $\sqrt[2]{121}$
Thinking: What number times itself is 121? ($11 \times 11 = 121$)
Answer: 11

20) $\sqrt[2]{64}$
Thinking: What number times itself is 64? ($8 \times 8 = 64$)
Answer: 8

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Part C: Find the answer.

*These problems ask for cube roots ($\sqrt[3]{}$). You need to find a number that, when multiplied by itself three times, equals the number inside.*

21) $\sqrt[3]{8}$
Thinking: $2 \times 2 \times 2 = 8$.
Answer: 2

22) $\sqrt[3]{27}$
Thinking: $3 \times 3 \times 3 = 27$.
Answer: 3

23) $\sqrt[3]{125}$
Thinking: $5 \times 5 = 25$, and $25 \times 5 = 125$.
Answer: 5

24) $\sqrt[3]{1000}$
Thinking: $10 \times 10 \times 10 = 1000$.
Answer: 10

25) $\sqrt[3]{512}$
Thinking: Let's check 8. $8 \times 8 = 64$, and $64 \times 8 = 512$.
Answer: 8

26) $\sqrt[3]{125}$
Thinking: Same as question 23. $5 \times 5 \times 5 = 125$.
Answer: 5

27) $\sqrt[3]{64}$
Thinking: $4 \times 4 = 16$, and $16 \times 4 = 64$.
Answer: 4

28) $\sqrt[3]{343}$
Thinking: Let's check 7. $7 \times 7 = 49$, and $49 \times 7 = 343$.
Answer: 7

29) $\sqrt[3]{729}$
Thinking: Let's check 9. $9 \times 9 = 81$, and $81 \times 9 = 729$.
Answer: 9

30) $\sqrt[3]{216}$
Thinking: Let's check 6. $6 \times 6 = 36$, and $36 \times 6 = 216$.
Answer: 6

Final Answer:
A.
1) 4
2) 16
3) 9
4) 64
5) 25
6) 1000
7) 144
8) 512
9) 49
10) 64

B.
11) 4
12) 5
13) 10
14) 9
15) 12
16) 40
17) 90
18) 7
19) 11
20) 8

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