# Find the smallest

(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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