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Chapter3 6 ½ –

Square and Square Root

Introduction Thus “All square numbers are perfect squares” but
all perfect squares may not be square numbers.
If a number is multiplied by itself the product
so formed is called the square of that number. Squares of some num bers are given be low :
In this chapter we will learn about the square
No. Square No. Square
and square root of numbers.
1 2 = 1 ´ 1 = 1 2 2 = 2 ´ 2 = 4
Square of a Number
3 2 = 3 ´ 3 = 9 4 2 = 4 ´ 4 = 16
The square of a number is that number which
raised to the power 2. 5 2 = 5 ´ 5 = 25 6 2 = 6 ´ 6 = 36
Thus, if ‘a’ is a number, then the square of a is 7 2 = 7 ´ 7 = 49 8 2 = 8 ´ 8 = 64
2
2
written as a and is given by a = a ´ a. 9 2 = 9 ´ 9 = 81 10 2 = 10 ´ 10 = 100
So, the square of a number is obtained by 11 2 = 11 ´ 11 = 121 12 2 = 12 ´ 12 = 144
multiplying it once, by itself. 13 2 = 13 ´ 13 = 169 14 2 = 14 ´ 14 = 196
2
If a ´ a = b i.e. a = b, then we say that the
15 2 = 15 ´ 15 = 225 16 2 = 16 ´ 16 = 256
square of number a is number b or the number b
is the square of number a. Let see the examples 17 2 =17 ´ 17 = 289 18 2 = 18 ´ 18 = 324
below: 19 2 = 19 ´ 19 = 361 20 2 = 20 ´ 20 = 400
2
)
v 2 = ( 2 ´ 2 = 4 and we say that the square 21 2 = 21 ´ 21 = 441 22 2 = 22 ´ 22 = 484
of 2 is 4. 23 2 = 23 23 = 529 24 2 = 24 ´ 24 = 576
´
2
=
)
´
v 3 = ( 3 ´ 3 = 9 and we say that the square 25 2 = 25 25 625 26 2 = 26 ´ 26 = 676
of 3 is 9. 27 2 = 27 27 = 729 28 2 =28 ´ 28 = 784
´
2
.
5
.
.
( . ) = 05 ´ 05 = 025 29 2 = 29 29 = 841 30 2 = 30 ´ 30 = 900
0
´
and
2 Procedure to check whether a given
æ 2ö 2 2 4
ç ÷ = ´ =
è 3ø 3 3 9 natural number is a perfect squares or not.
2
´
v (-2 ) = ((-2 ) (-2 )) = 4 and we say that Step I: Obtain the natural number.
Step II: Write the number as a product of
the square of (-2) is 4.
prime factors.
2
´
v (-3 ) = ((-3 ) (-3 )) = 9 and we say that
Step III: Group the factors into pairs of like
the square of (-3) is 9.
factors.
Perfect square: Step IV: See whether some factors are left
A rational number that is equal to the square over or not. If no fac tor is left in the
of another rational number, is called perfect group ing, then the given num ber is
square. This number is exact square and do a per fect square. Oth er wise, it is not
not involve decimal or fractions. a per fect-square.

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Mathematics In Focus - 8