Q. 244.0( 5 Votes )

Find the smallest

Answer :

(i) 23805


Resolving 23805 into prime factors, we get


23805 = 3 × 3 × 23 × 23 × 5


Obtained factors can be paired into equal factors except for 5


To pair it equally multiply with 5


23805 × 5 = 3 × 3 × 5 × 5 × 23 × 23


Again,


23805 × 5 = (3× 5 × 23) × (3 × 5 × 23)


= 345 × 345


= (345)2


Therefore, product is the square of 345


(ii) 12150


Resolving 12150 into prime factors, we get


12150 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 × 2


Obtained factors can be paired into equal factors except for 2


To pair it equally multiply with 2


12150 × 2 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 3 × 3


Again,


12150 × 2 = (5 × 3 × 2 × 2 × 2) × (5 × 3 × 2 × 2 × 2)


= 120 × 120


= (120)2


Therefore, product is the square of 120


(iii) 7688


Resolving 7688 into prime factors, we get


7688 = 2 × 2 × 31 × 31 × 2


Obtained factors can be paired into equal factors except for 2


To pair it equally multiply with 2


7688 × 2 = 2 × 2 × 2 × 2 × 31 × 31


Again,


7688 × 2 = (2× 2 × 31) × (2 × 2 × 31)


= 124 × 124


= (124)2


Therefore, product is the square of 124

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