By what least number should the given number be divided to get a perfect square number? In each case, find the number whose square is the new number.
(i) 1575 (ii) 9075
(iii) 4851 (iv) 3380
(v) 4500 (vi) 7776
(vii) 8820 (viii) 4056
(i) 1575
At first,
We’ll resolve the given number into prime factors:
Hence,
1575 = 7 × 25 × 9
= 7 × 3 × 3 × 5 × 5
= (5 × 3) × (5 × 3) × 7
In the above factors only 7 is unpaired
So, in order to get a perfect square the given number should be divided by 7
Hence,
The number whose perfect square is the new number is as following:
= (5 × 3) × (5 × 3)
= (5 × 3) × (5 × 3)
= (5 × 3)2
= (15)2
At first,
We’ll resolve the given number into prime factors:
Hence,
9075 = 121 × 25 × 3
= 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 divided by 3
Hence,
The number whose perfect square is the new number is as following:
=(5 × 11) × (5 × 11)
= (5 × 11)2
= (55)2
At first,
We’ll resolve the given number into prime factors:
Hence,
4851 = 11 × 49 × 9
= 11 × 3 × 3 × 7 × 7
= (7 × 3) × (7 × 3) × 11
In the above factors only 11 is unpaired
So, in order to get a perfect square the given number should be divided by 11
Hence,
The number whose perfect square is the new number is as following:
=(7 × 3) × (7 × 3)
= (7 × 3)2
= (21)2
At first,
We’ll resolve the given number into prime factors:
Hence,
3380 = 4 × 5 × 169
= 2 × 13 × 13 × 2 × 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 divided by 5
Hence,
The number whose perfect square is the new number is as following:
=(2 × 13) × (2 × 13)
= (2 × 13)2
= (26)2
At first,
We’ll resolve the given number into prime factors:
Hence,
4500 = 4 × 125 × 9
= 2 × 2 × 3 × 3 × 5 × 5 × 5
= (5 × 3 × 2) × (5 × 3 × 2) × 5
In the above factors only 5 is unpaired
So, in order to get a perfect square the given number should be divided by 5
Hence,
The number whose perfect square is the new number is as following:
=(5 × 3 × 2) × (5 × 3 × 2)
= (5 × 2 × 3) × (5 × 2 × 3)
= (5 × 2 × 3)2
= (30)2
At first,
We’ll resolve the given number into prime factors:
Hence,
7776 = 32 × 243
= 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 2
= (2 × 2 × 3 × 3) × (2 × 2 × 3 × 3) × 2 × 3
In the above factors only 2 and 3 are unpaired
So, in order to get a perfect square the given number should be divided by 6
Hence,
The number whose perfect square is the new number is as following:
= (2 × 2 × 3 × 3) × (2 × 2 × 3 × 3)
= (2 × 2 × 3 × 3)2
= (36)2
At first,
We’ll resolve the given number into prime factors:
Hence,
8820 = 4 × 5 × 9 × 49
= 2 × 2 × 3 × 3 × 7 × 7 × 5
= (7 × 3 × 2) × (7 × 3 × 2) × 5
In the above factors only 5 is unpaired
So, in order to get a perfect square the given number should be divided by 5
Hence,
The number whose perfect square is the new number is as following:
=(7 × 3 × 2) × (7 × 3 × 2)
= (7 × 3 × 2)2
= (42)2
At first,
We’ll resolve the given number into prime factors:
Hence,
4056 = 8 × 3 × 169
= 2 × 2 × 13 × 13 × 3 × 2
= (13 × 2) × (13 × 2) × 6
In the above factors only 6 is unpaired
So, in order to get a perfect square, the given number should be divided by 6
Hence,
The number whose perfect square is the new number is as following:
=(13 × 2) × (13 × 2)
= (13 × 2)2
= (26)2