By what least num

(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

(ii) 9075

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

(iii) 4851

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

(iv) 3380

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

(v) 4500

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

(vi) 7776

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

(vii) 8820

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

(viii) 4056

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