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Number - Square and Cube Numbers

Grade 6IB

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

🔑Concepts

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A square number is the product of an integer multiplied by itself. It is denoted by the exponent 22, written as n2n^2.

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A cube number is the product of an integer multiplied by itself three times. It is denoted by the exponent 33, written as n3n^3.

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Square numbers can be represented visually as the area of a square with side length nn, while cube numbers represent the volume of a cube with side length nn.

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The square root n\sqrt{n} is the inverse operation of squaring. For example, since 62=366^2 = 36, then 36=6\sqrt{36} = 6.

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The cube root n3\sqrt[3]{n} is the inverse operation of cubing. For example, since 43=644^3 = 64, then 643=4\sqrt[3]{64} = 4.

📐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

n2=n\sqrt{n^2} = n

n33=n\sqrt[3]{n^3} = n

💡Examples

Problem 1:

Calculate the value of 15215^2.

Solution:

15×1575150225\begin{array}{r} 15 \\ \times 15 \\ \hline 75 \\ 150 \\ \hline 225 \end{array}

Explanation:

To find 15215^2, we multiply 1515 by itself (15×1515 \times 15). Using vertical multiplication, we find the result is 225225.

Problem 2:

Find the cube of 66.

Solution:

63=6×6×6=36×6=2166^3 = 6 \times 6 \times 6 = 36 \times 6 = 216

Explanation:

To cube a number, multiply it by itself twice. First, 6×6=366 \times 6 = 36. Then, 36×6=21636 \times 6 = 216.

Problem 3:

Determine the value of 81+83\sqrt{81} + \sqrt[3]{8}.

Solution:

9+2=119 + 2 = 11

Explanation:

The square root of 8181 is 99 because 92=819^2 = 81. The cube root of 88 is 22 because 23=82^3 = 8. Adding them together gives 9+2=119 + 2 = 11.

Problem 4:

A wooden cube has a side length of 4 cm4\text{ cm}. Calculate its volume.

Solution:

Volume=43=4×4×4=64 cm3\text{Volume} = 4^3 = 4 \times 4 \times 4 = 64\text{ cm}^3

Explanation:

The volume of a cube is calculated by cubing its side length (s3s^3). Since the side is 4 cm4\text{ cm}, the volume is 64 cubic centimeters64\text{ cubic centimeters}.