Step-by-step explanation:

3 question

(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

(ii) 2156

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

(iii) 3332

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

(iv) 2925

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

(v) 9075

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

(vi) 7623  

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

(vii) 3380

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

(viii) 2475  

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

4 question

In each CASE, find the number whose square is the new number. THUS, to get a perfect square number, the given number should be divided by 7. Hence, the number whose square is the new number = 15. Thus, to get a perfect square number, the given number should be divided by 3

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