Page 40 - ICSE Math 8

3 Squares and Square Roots

Key Concepts

• Square of a Number • Finding Square Root by Prime Factorization Method
• Perfect Squares or Square Numbers • Finding Square Root by Long Division Method
• Prime Factorization Method • Square Root of a Fraction
• Properties and Patterns of Perfect Squares • Square Roots of Rational Numbers in Decimal Form
• Square Roots • Approximating the Value of Square Roots by Long
• Finding Square Root by Repeated Subtraction Division Method
Method

Square of a Number

A number multiplied by itself is called the square of a number.
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For example, 2 × 2 = 4. Here, 4 is the square of 2 and is written as 2 = 4. Try These
It is read as ‘2 raised to the power 2 is 4’. Consider some more examples of
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square of a number. 1. 16 = _____, and is read as
______________________.
2
(i) 11 = 11 × 11 = 121 (read as ‘11 raised to the power 2’ is 121) 2
2. –4 = _____, and is read as
3 2 3 3 9 7
2
(ii) = × = (iii) (0.04) = 0.04 × 0.04 = 0.0016 _______________________.
5 5 5 25
2
2
(iv) (–6) = (–6) × (–6) = 36 (v) (100) = 100 × 100 = 10,000 and so on.
Thus, the square of a number is the number raised to the power 2.

Perfect Squares or Square Numbers
A rational number is said to be a perfect square or a square number it if is Maths Info
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the square of a natural number. For example, 9 = 3 × 3 = 3 . Thus, 9 is a
perfect square or a square number. A perfect square number
is always expressible as the
Let us now discuss a method to check whether a number is perfect square product of pairs of equal
or not. factors.

Prime Factorization Method Try This

To check if a given natural number is a perfect square, follow these steps: Write the first 5 perfect square
1. Write the given number as a product of its prime factors. numbers.
2. Arrange the prime factors in pairs. If no factor is left after pairing, the given natural number is a perfect
square, otherwise not.
5 625
Example 1: Is 625 a perfect square?
5 125
Solution: To find whether 625 is a perfect square or not, write the number as a 5 25
product of its prime factors.
5 5
\ 625 = 5 × 5 × 5 × 5 1
Since no factor is left unpaired, hence 625 is a perfect square.

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