Square Roots and Cube Roots | Interactive Worksheet - Free Printable

Absolutely! Let’s solve this worksheet step by step. The worksheet teaches squares, cubes, and their roots.

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## 🔷 Part 1: Understanding the Definitions

- Square of a number = number × itself → \( n^2 = n \times n \)
- Example: \( 5^2 = 5 \times 5 = 25 \)

- Cube of a number = number × number × number → \( n^3 = n \times n \times n \)
- Example: \( 5^3 = 5 \times 5 \times 5 = 125 \)

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## ✔ Part 2: Write the square or cube of each number

We’ll compute each one:

A. \( 4^2 = 4 \times 4 = \boxed{16} \)

B. \( 6^2 = 6 \times 6 = \boxed{36} \)

C. \( 10^2 = 10 \times 10 = \boxed{100} \)

D. \( 20^2 = 20 \times 20 = \boxed{400} \)

E. \( 8^2 = 8 \times 8 = \boxed{64} \)

F. \( 17^2 = 17 \times 17 = \boxed{289} \)

*(17×17: 10×17=170, 7×17=119 → 170+119=289)*

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G. \( 9^2 = 9 \times 9 = \boxed{81} \)

H. \( 7^2 = 7 \times 7 = \boxed{49} \)

I. \( 5^2 = 5 \times 5 = \boxed{25} \)

J. \( 24^2 = 24 \times 24 = \boxed{576} \)

*(24×24: (20+4)² = 400 + 160 + 16 = 576)*

K. \( 13^2 = 13 \times 13 = \boxed{169} \)

*(13×13: 10×13=130, 3×13=39 → 130+39=169)*

L. \( 25^2 = 25 \times 25 = \boxed{625} \)

*(25² is a common square: 625)*

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M. \( 3^3 = 3 \times 3 \times 3 = \boxed{27} \)

N. \( 15^3 = 15 \times 15 \times 15 = 225 \times 15 = \boxed{3,375} \)

*(15×15=225; 225×15: 200×15=3000, 25×15=375 → 3000+375=3375)*

O. \( 14^3 = 14 \times 14 \times 14 = 196 \times 14 = \boxed{2,744} \)

*(14×14=196; 196×14: 200×14=2800 minus 4×14=56 → 2800-56=2744)*

P. \( 19^3 = 19 \times 19 \times 19 = 361 \times 19 = \boxed{6,859} \)

*(19×19=361; 361×19: 361×20=7220 minus 361 → 7220-361=6859)*

Q. \( 48^3 = 48 \times 48 \times 48 = 2,304 \times 48 = \boxed{110,592} \)

*(48×48=2304; 2304×48: break into 2304×50=115,200 minus 2304×2=4608 → 115,200-4608=110,592)*

R. \( 37^3 = 37 \times 37 \times 37 = 1,369 \times 37 = \boxed{50,653} \)

*(37×37=1369; 1369×37: 1369×30=41,070; 1369×7=9,583 → 41,070+9,583=50,653)*

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## ✔ Part 3: Write the square root

Square root of a number = what number squared gives that number?
Example: \( \sqrt{64} = 8 \) because \( 8^2 = 64 \)

G. \( \sqrt{36} = \boxed{6} \)

\( \sqrt{64} = \boxed{8} \)

\( \sqrt{81} = \boxed{9} \)

\( \sqrt{25} = \boxed{5} \)

\( \sqrt{324} = \boxed{18} \) *(18²=324)*

\( \sqrt{529} = \boxed{23} \) *(23²=529)*

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H. \( \sqrt{100} = \boxed{10} \)

\( \sqrt{49} = \boxed{7} \)

\( \sqrt{4} = \boxed{2} \)

\( \sqrt{16} = \boxed{4} \)

\( \sqrt{121} = \boxed{11} \)

\( \sqrt{1,600} = \boxed{40} \) *(40²=1600)*

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I. \( \sqrt{400} = \boxed{20} \)

\( \sqrt{225} = \boxed{15} \)

\( \sqrt{625} = \boxed{25} \)

\( \sqrt{144} = \boxed{12} \)

\( \sqrt{900} = \boxed{30} \)

\( \sqrt{2,500} = \boxed{50} \) *(50²=2500)*

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## ✔ Part 4: Write the cube root

Cube root of a number = what number cubed gives that number?
Example: \( \sqrt[3]{125} = 5 \) because \( 5^3 = 125 \)

J. \( \sqrt[3]{125} = \boxed{5} \)

\( \sqrt[3]{1,000} = \boxed{10} \) *(10³=1000)*

\( \sqrt[3]{64} = \boxed{4} \) *(4³=64)*

\( \sqrt[3]{27} = \boxed{3} \)

\( \sqrt[3]{8} = \boxed{2} \)

\( \sqrt[3]{216} = \boxed{6} \) *(6³=216)*

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K. \( \sqrt[3]{512} = \boxed{8} \) *(8³=512)*

\( \sqrt[3]{1,728} = \boxed{12} \) *(12³=1728)*

\( \sqrt[3]{2,744} = \boxed{14} \) *(from earlier: 14³=2744)*

\( \sqrt[3]{343} = \boxed{7} \) *(7³=343)*

\( \sqrt[3]{8,000} = \boxed{20} \) *(20³=8000)*

\( \sqrt[3]{6,859} = \boxed{19} \) *(from earlier: 19³=6859)*

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## 📝 Final Answer Key:

Part 2: Squares & Cubes

A. 16
B. 36
C. 100
D. 400
E. 64
F. 289
G. 81
H. 49
I. 25
J. 576
K. 169
L. 625
M. 27
N. 3,375
O. 2,744
P. 6,859
Q. 110,592
R. 50,653

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Part 3: Square Roots

G. 6, 8, 9, 5, 18, 23
H. 10, 7, 2, 4, 11, 40
I. 20, 15, 25, 12, 30, 50

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Part 4: Cube Roots

J. 5, 10, 4, 3, 2, 6
K. 8, 12, 14, 7, 20, 19

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✔ All problems solved! This worksheet reinforces exponents and roots — essential for algebra and higher math. Great practice!