Exponent, square root, and cube root practice problems for math students.
Math worksheet with problems on exponents, square roots, and cube roots, including examples and instructions to show working.
JPG
1000×1413
85 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #202129
⭐
Show Answer Key & Explanations
Step-by-step solution for: Square and Cube roots of numbers | Simplifying square and cube
▼
Show Answer Key & Explanations
Step-by-step solution for: Square and Cube roots of numbers | Simplifying square and cube
Here is the complete solution to all 30 problems, with clear working shown for each.
---
## A. Exponents
Example:
$2^2 = 2 \times 2 = 4$
---
1) $2^4 =$
$2^4 = 2 \times 2 \times 2 \times 2 = 16$
✔ Answer: 16
---
2) $-3^2 =$
⚠️ Important: This is not $(-3)^2$. The negative sign is *outside* the exponentiation.
So, $-3^2 = -(3 \times 3) = -9$
✔ Answer: -9
---
3) $4^3 =$
$4^3 = 4 \times 4 \times 4 = 64$
✔ Answer: 64
---
4) $(-5)^2 =$
Negative base with even exponent → positive result.
$(-5)^2 = (-5) \times (-5) = 25$
✔ Answer: 25
---
5) $10^3 =$
$10^3 = 10 \times 10 \times 10 = 1000$
✔ Answer: 1000
---
6) $12^2 =$
$12^2 = 12 \times 12 = 144$
✔ Answer: 144
---
7) $(-8)^3 =$
Negative base with odd exponent → negative result.
$(-8)^3 = (-8) \times (-8) \times (-8) = 64 \times (-8) = -512$
✔ Answer: -512
---
8) $7^2 =$
$7^2 = 7 \times 7 = 49$
✔ Answer: 49
---
## B. Square Roots (√)
> Note: In real numbers, square root of a negative number is IMPOSSIBLE (undefined).
---
11) $\sqrt{16} = 4$ *(given as example)*
✔ Answer: 4
---
12) $\sqrt{25} =$
What number squared is 25? $5 \times 5 = 25$
✔ Answer: 5
---
13) $\sqrt{-100} =$
Square root of a negative number → not real.
✔ Answer: IMPOSSIBLE
---
14) $\sqrt{81} =$
$9 \times 9 = 81$
✔ Answer: 9
---
15) $\sqrt{144} =$
$12 \times 12 = 144$
✔ Answer: 12
---
16) $\sqrt{1600} =$
$40 \times 40 = 1600$
✔ Answer: 40
---
17) $\sqrt{8100} =$
$90 \times 90 = 8100$
✔ Answer: 90
---
18) $\sqrt{49} =$
$7 \times 7 = 49$
✔ Answer: 7
---
19) $\sqrt{121} =$
$11 \times 11 = 121$
✔ Answer: 11
---
20) $\sqrt{-64} =$
Negative under square root → not real.
✔ Answer: IMPOSSIBLE
---
## C. Cube Roots ($\sqrt[3]{}$)
> Note: Cube roots are defined for all real numbers, including negatives. Odd roots of negatives are negative.
---
21) $\sqrt[3]{8} =$
What number cubed is 8? $2 \times 2 \times 2 = 8$
✔ Answer: 2
---
22) $\sqrt[3]{27} =$
$3 \times 3 \times 3 = 27$
✔ Answer: 3
---
23) $\sqrt[3]{125} =$
$5 \times 5 \times 5 = 125$
✔ Answer: 5
---
24) $\sqrt[3]{1000} =$
$10 \times 10 \times 10 = 1000$
✔ Answer: 10
---
25) $\sqrt[3]{-512} =$
Cube root of negative is negative.
$(-8) \times (-8) \times (-8) = -512$
✔ Answer: -8
---
26) $\sqrt[3]{-125} =$
$(-5) \times (-5) \times (-5) = -125$
✔ Answer: -5
---
27) $\sqrt[3]{64} =$
$4 \times 4 \times 4 = 64$
✔ Answer: 4
---
28) $\sqrt[3]{343} =$
$7 \times 7 \times 7 = 343$
✔ Answer: 7
---
29) $\sqrt[3]{729} =$
$9 \times 9 \times 9 = 729$
✔ Answer: 9
---
30) $\sqrt[3]{216} =$
$6 \times 6 \times 6 = 216$
✔ Answer: 6
---
## ✔ Final Answers Summary:
1) 16
2) -9
3) 64
4) 25
5) 1000
6) 144
7) -512
8) 49
11) 4
12) 5
13) IMPOSSIBLE
14) 9
15) 12
16) 40
17) 90
18) 7
19) 11
20) IMPOSSIBLE
21) 2
22) 3
23) 5
24) 10
25) -8
26) -5
27) 4
28) 7
29) 9
30) 6
Let me know if you’d like these explained further!
---
## A. Exponents
Example:
$2^2 = 2 \times 2 = 4$
---
1) $2^4 =$
$2^4 = 2 \times 2 \times 2 \times 2 = 16$
✔ Answer: 16
---
2) $-3^2 =$
⚠️ Important: This is not $(-3)^2$. The negative sign is *outside* the exponentiation.
So, $-3^2 = -(3 \times 3) = -9$
✔ Answer: -9
---
3) $4^3 =$
$4^3 = 4 \times 4 \times 4 = 64$
✔ Answer: 64
---
4) $(-5)^2 =$
Negative base with even exponent → positive result.
$(-5)^2 = (-5) \times (-5) = 25$
✔ Answer: 25
---
5) $10^3 =$
$10^3 = 10 \times 10 \times 10 = 1000$
✔ Answer: 1000
---
6) $12^2 =$
$12^2 = 12 \times 12 = 144$
✔ Answer: 144
---
7) $(-8)^3 =$
Negative base with odd exponent → negative result.
$(-8)^3 = (-8) \times (-8) \times (-8) = 64 \times (-8) = -512$
✔ Answer: -512
---
8) $7^2 =$
$7^2 = 7 \times 7 = 49$
✔ Answer: 49
---
## B. Square Roots (√)
> Note: In real numbers, square root of a negative number is IMPOSSIBLE (undefined).
---
11) $\sqrt{16} = 4$ *(given as example)*
✔ Answer: 4
---
12) $\sqrt{25} =$
What number squared is 25? $5 \times 5 = 25$
✔ Answer: 5
---
13) $\sqrt{-100} =$
Square root of a negative number → not real.
✔ Answer: IMPOSSIBLE
---
14) $\sqrt{81} =$
$9 \times 9 = 81$
✔ Answer: 9
---
15) $\sqrt{144} =$
$12 \times 12 = 144$
✔ Answer: 12
---
16) $\sqrt{1600} =$
$40 \times 40 = 1600$
✔ Answer: 40
---
17) $\sqrt{8100} =$
$90 \times 90 = 8100$
✔ Answer: 90
---
18) $\sqrt{49} =$
$7 \times 7 = 49$
✔ Answer: 7
---
19) $\sqrt{121} =$
$11 \times 11 = 121$
✔ Answer: 11
---
20) $\sqrt{-64} =$
Negative under square root → not real.
✔ Answer: IMPOSSIBLE
---
## C. Cube Roots ($\sqrt[3]{}$)
> Note: Cube roots are defined for all real numbers, including negatives. Odd roots of negatives are negative.
---
21) $\sqrt[3]{8} =$
What number cubed is 8? $2 \times 2 \times 2 = 8$
✔ Answer: 2
---
22) $\sqrt[3]{27} =$
$3 \times 3 \times 3 = 27$
✔ Answer: 3
---
23) $\sqrt[3]{125} =$
$5 \times 5 \times 5 = 125$
✔ Answer: 5
---
24) $\sqrt[3]{1000} =$
$10 \times 10 \times 10 = 1000$
✔ Answer: 10
---
25) $\sqrt[3]{-512} =$
Cube root of negative is negative.
$(-8) \times (-8) \times (-8) = -512$
✔ Answer: -8
---
26) $\sqrt[3]{-125} =$
$(-5) \times (-5) \times (-5) = -125$
✔ Answer: -5
---
27) $\sqrt[3]{64} =$
$4 \times 4 \times 4 = 64$
✔ Answer: 4
---
28) $\sqrt[3]{343} =$
$7 \times 7 \times 7 = 343$
✔ Answer: 7
---
29) $\sqrt[3]{729} =$
$9 \times 9 \times 9 = 729$
✔ Answer: 9
---
30) $\sqrt[3]{216} =$
$6 \times 6 \times 6 = 216$
✔ Answer: 6
---
## ✔ Final Answers Summary:
A. Exponents:
1) 16
2) -9
3) 64
4) 25
5) 1000
6) 144
7) -512
8) 49
B. Square Roots:
11) 4
12) 5
13) IMPOSSIBLE
14) 9
15) 12
16) 40
17) 90
18) 7
19) 11
20) IMPOSSIBLE
C. Cube Roots:
21) 2
22) 3
23) 5
24) 10
25) -8
26) -5
27) 4
28) 7
29) 9
30) 6
Let me know if you’d like these explained further!
Parent Tip: Review the logic above to help your child master the concept of cubed roots worksheets.
