Question

EXAMPLE 3
Show that
that 6292 is not a per
Solution
equal factors.
do prime factors, we get
11-13 (2" 11" 13).
be expressed as a product of pairs of equal fa
et a perfect square
Property 1. A number e
EXAMPLES
The number
So nowe
EXAMPLE 4
ce 6292 is not a perfect square
er should 3675 be multiplied to get a perfect
Conose square is the new number.
Solution
Resolving 6292 into prime
6292 -2 211
Thus, 6292 cannot be exp
Hence, 6292 is not
By what leasi number sho
Also find the number
Resolving 3675 into p
3675 = 3x5x57x7 - 10
Thus, to get a perfect squa
should be multiplied by 3.
New number =(32x52x7°) - lo
Hence, the number whose squar
By what least number should 6
Find the number whose squar
Property 2. A ruumber
EXAMPLES The num
respectiv
So, non
ug 3675 into prime factors. We
7x7 = (3x5x7").
cl square number, the given number
Property 3. If a nu
squar
fect square num
umbe EXAMPLES 170.
EXAMPLE 5.
S *7)-(3x5 7) = (105)
se square is the new number = 105.
er should 6300 be divided to get a perfect sau
nose square is the new number.
31 6. Property 4. If ar
sque
EXAMPLES 578
Solution
Resolving 6300 into primo
8 0300 into prime factors, we get
0300 = 3x3 x 7x5x5x2 x 2 = (
3x70
c7/07/
Property 5. TH
7*5*5*2*2 = (32 x 7x52 x 2").
" Square number, the given number
EXAMPLES
2
Thus, to get a perfect square
should be divided by 7.
wew number obtained = (32 x 5 x 21
Hence, the number whose square 1
Property 6.
***5*22) = (3 x 5 x 2)2 = (30)2
nose square is the new number = 30.
EXAMPLES
Property 7.
bers are perts EXAMPLE
EXERCISE 3A
Prime factorisation method, find which of the following numbers are
1. Using the prime factorisation m
squares:
(1) 441
(ii) 576
(v) 5625
(vi) 9075
Property
(iii) 11025
(vii) 4225
(iv) 1176
(viii) 1089
mure In each case, find the​

Answer 1

squares:

(1) 441

(ii) 576

(v) 5625

(vi) 9075

Property

(iii) 11025

(vii) 4225

(iv) 1176

(viii) 1089