Grade 8 Cubes and Cube Roots Worksheets - WorkSheets Buddy - Free Printable

Let's solve the worksheet step by step and explain each part.

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Understanding the Concepts

1. Square of a number: Multiply the number by itself.
- Example: $ 5^2 = 5 \times 5 = 25 $

2. Cube of a number: Multiply the number by itself three times.
- Example: $ 5^3 = 5 \times 5 \times 5 = 125 $

3. Square root: The inverse of squaring. It’s the number that, when multiplied by itself, gives the original number.
- Example: $ \sqrt{25} = 5 $ because $ 5 \times 5 = 25 $

4. Cube root: The inverse of cubing. It’s the number that, when multiplied by itself three times, gives the original number.
- Example: $ \sqrt[3]{125} = 5 $ because $ 5 \times 5 \times 5 = 125 $

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Part 1: Write the square or cube of each number

#### Squares (x²):
1) $ 13^2 = 13 \times 13 = \boxed{169} $
2) $ 4^2 = 4 \times 4 = \boxed{16} $
3) $ 9^2 = 9 \times 9 = \boxed{81} $

#### Cubes (x³):
4) $ 5^3 = 5 \times 5 \times 5 = \boxed{125} $
5) $ 2^3 = 2 \times 2 \times 2 = \boxed{8} $
6) $ 6^3 = 6 \times 6 \times 6 = \boxed{216} $

#### More Squares and Cubes:
7) $ 48^2 = 48 \times 48 = \boxed{2304} $
8) $ 3^3 = 3 \times 3 \times 3 = \boxed{27} $
9) $ 7^3 = 7 \times 7 \times 7 = \boxed{343} $

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Part 2: Write the square root of each number

We are looking for the number that, when squared, gives the given number.

1) $ \sqrt{16} = \boxed{4} $ because $ 4 \times 4 = 16 $
2) $ \sqrt{9} = \boxed{3} $ because $ 3 \times 3 = 9 $
3) $ \sqrt{25} = \boxed{5} $ because $ 5 \times 5 = 25 $
4) $ \sqrt{81} = \boxed{9} $ because $ 9 \times 9 = 81 $
5) $ \sqrt{1} = \boxed{1} $ because $ 1 \times 1 = 1 $
6) $ \sqrt{4} = \boxed{2} $ because $ 2 \times 2 = 4 $
7) $ \sqrt{49} = \boxed{7} $ because $ 7 \times 7 = 49 $
8) $ \sqrt{36} = \boxed{6} $ because $ 6 \times 6 = 36 $
9) $ \sqrt{100} = \boxed{10} $ because $ 10 \times 10 = 100 $

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Part 3: Write the cube root of each number

We are looking for the number that, when cubed, gives the given number.

1) $ \sqrt[3]{64} = \boxed{4} $ because $ 4 \times 4 \times 4 = 64 $
2) $ \sqrt[3]{1} = \boxed{1} $ because $ 1 \times 1 \times 1 = 1 $
3) $ \sqrt[3]{125} = \boxed{5} $ because $ 5 \times 5 \times 5 = 125 $
4) $ \sqrt[3]{216} = \boxed{6} $ because $ 6 \times 6 \times 6 = 216 $
5) $ \sqrt[3]{8} = \boxed{2} $ because $ 2 \times 2 \times 2 = 8 $
6) $ \sqrt[3]{1,728} = \boxed{12} $ because $ 12 \times 12 \times 12 = 1,728 $
7) $ \sqrt[3]{343} = \boxed{7} $ because $ 7 \times 7 \times 7 = 343 $
8) $ \sqrt[3]{0} = \boxed{0} $ because $ 0 \times 0 \times 0 = 0 $
9) $ \sqrt[3]{729} = \boxed{9} $ because $ 9 \times 9 \times 9 = 729 $

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✔ Final Answers:

#### Part 1: Squares and Cubes
1) 169
2) 16
3) 81
4) 125
5) 8
6) 216
7) 2304
8) 27
9) 343

#### Part 2: Square Roots
1) 4
2) 3
3) 5
4) 9
5) 1
6) 2
7) 7
8) 6
9) 10

#### Part 3: Cube Roots
1) 4
2) 1
3) 5
4) 6
5) 2
6) 12
7) 7
8) 0
9) 9

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