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Number System - Square and cube numbers

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A square number is the result of multiplying a whole number by itself (e.g., 3×3=93 \times 3 = 9).

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Square numbers can be represented visually as a square arrangement of dots.

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A cube number is the result of multiplying a whole number by itself and then by itself again (e.g., 2×2×2=82 \times 2 \times 2 = 8).

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The notation for squaring a number is n2n^2, and for cubing a number is n3n^3.

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The inverse (opposite) of squaring a number is finding the square root (x\sqrt{x}).

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The inverse of cubing a number is finding the cube root (x3\sqrt[3]{x}).

📐Formulae

n2=n×nn^2 = n \times n

n3=n×n×nn^3 = n \times n \times n

Area of a Square=s2\text{Area of a Square} = s^2

Volume of a Cube=s3\text{Volume of a Cube} = s^3

💡Examples

Problem 1:

Calculate 828^2 and 434^3.

Solution:

82=648^2 = 64 and 43=644^3 = 64.

Explanation:

To find 828^2, multiply 8 by itself: 8×8=648 \times 8 = 64. To find 434^3, multiply 4 by itself three times: 4×4×4=16×4=644 \times 4 \times 4 = 16 \times 4 = 64.

Problem 2:

Identify the square number that lies between 20 and 30.

Solution:

25

Explanation:

List the squares: 42=164^2 = 16, 52=255^2 = 25, 62=366^2 = 36. The only square number between 20 and 30 is 25.

Problem 3:

If the volume of a cube is 27 cm327 \text{ cm}^3, what is the length of one side?

Solution:

3 cm3 \text{ cm}

Explanation:

The formula for volume is V=s3V = s^3. We need to find which number multiplied by itself three times equals 27. Since 3×3×3=273 \times 3 \times 3 = 27, the side length is 3 cm.

Problem 4:

Find the value of 49+1253\sqrt{49} + \sqrt[3]{125}.

Solution:

12

Explanation:

The square root of 49 is 7 (because 7×7=497 \times 7 = 49). The cube root of 125 is 5 (because 5×5×5=1255 \times 5 \times 5 = 125). Therefore, 7+5=127 + 5 = 12.