By what least number should the given number be multiplied to get a perfect square number? In each case, find the number whose square is the new number.
(i) 3675 (ii) 2156
(iii) 3332 (iv) 2925
(v) 9075 (vi) 7623
(vii) 3380 (viii) 2475
(i) 3675
At first,
We’ll resolve the given number into prime factors:
Hence,
3675 = 3 × 25 × 49
= 7 × 7 × 3 × 5 × 5
= (5 × 7) × (5 × 7) × 3
In the above factors only 3 is unpaired
So, in order to get a perfect square the given number should be multiplied by 3
Hence,
The number whose perfect square is the new number is as following:
= (5 × 7) × (5 × 7) × 3 × 3
= (5 × 7 × 3) × (5 × 7 × 3)
= (5 × 7 × 3)2
= (105)2
At first,
We’ll resolve the given number into prime factors:
Hence,
2156 = 4 × 11 × 49
= 7 × 7 × 2 × 2 × 11
= (2 × 7) × (2 × 7) × 11
In the above factors only 11 is unpaired
So, in order to get a perfect square the given number should be multiplied by 11
Hence,
The number whose perfect square is the new number is as following:
= (2 × 7) × (2 × 7) × 11 × 11
= (2 × 7 × 11) × (2 × 7 × 11)
= (5 × 7 × 11)2
= (154)2
At first,
We’ll resolve the given number into prime factors:
Hence,
3332 = 4 × 17 × 49
= 7 × 7 × 2 × 2 × 17
= (2 × 7) × (2 × 7) × 17
In the above factors only 17 is unpaired
So, in order to get a perfect square the given number should be multiplied by 17
Hence,
The number whose perfect square is the new number is as following:
= (2 × 7) × (2 × 7) × 17 × 17
= (2 × 7 × 17) × (2 × 7 × 17)
= (2 × 7 × 17)2
= (238)2
At first,
We’ll resolve the given number into prime factors:
Hence,
2925 = 9 × 25 × 13
= 3 × 3 × 13 × 5 × 5
= (5 × 3) × (5 × 3) × 13
In the above factors only 13 is unpaired
So, in order to get a perfect square the given number should be multiplied by 13
Hence,
The number whose perfect square is the new number is as following:
= (5 × 3) × (5 × 3) × 13 × 13
= (5 × 3 × 13) × (5 × 3 × 13)
= (5 × 3 × 13)2
= (195)2
At first,
We’ll resolve the given number into prime factors:
Hence,
9075 = 3 × 25 × 121
= 11 × 11 × 3 × 5 × 5
= (5 × 11) × (5 × 11) × 3
In the above factors only 3 is unpaired
So, in order to get a perfect square the given number should be multiplied by 3
Hence,
The number whose perfect square is the new number is as following:
= (5 × 11) × (5 × 11) × 3 × 3
= (5 × 11 × 3) × (5 × 11 × 3)
= (5 × 11 × 3)2
= (165)2
At first,
We’ll resolve the given number into prime factors:
Hence,
7623 = 9 × 7 × 121
= 7 × 3 × 3 × 11 × 11
= (11 × 3) × (11 × 3) × 7
In the above factors only 7 is unpaired
So, in order to get a perfect square the given number should be multiplied by 7
Hence,
The number whose perfect square is the new number is as following:
= (3 × 11) × (3 × 11) × 7 × 7
= (11 × 7 × 3) × (11 × 7 × 3)
= (11 × 7 × 3)2
= (231)2
At first,
We’ll resolve the given number into prime factors:
Hence,
3380 = 4 × 5 × 169
= 2 × 2 × 13 × 13 × 5
= (2 × 13) × (2 × 13) × 5
In the above factors only 5 is unpaired
So, in order to get a perfect square the given number should be multiplied by 5
Hence,
The number whose perfect square is the new number is as following:
= (2 × 13) × (2 × 13) × 5 × 5
= (5 × 2 × 13) × (5 × 2 × 13)
= (5 × 2 × 13)2
= (130)2
At first,
We’ll resolve the given number into prime factors:
Hence,
2475 = 11 × 25 × 9
= 11 × 3 × 3 × 5 × 5
= (5 × 3) × (5 × 3) × 11
In the above factors only 11 is unpaired
So, in order to get a perfect square the given number should be multiplied by 11
Hence,
The number whose perfect square is the new number is as following:
=(5 × 3) × (5 × 3) × 11 × 11
= (5 × 11 × 3) × (5 × 11 × 3)
= (5 × 11 × 3)2
= (165)2