Answer :

(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


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