Question

by what least number should we multiply 240 to make it perfect square

Answer 1

Hi your answer is,
240/5=48
48/3=16
16/2=8
8/2=4
4/2=2
240=2 x2x2x5x3
therefore 240 must be multiplied by 2,5and3 that is 30to make it a perfect square.

Answer 2

2 | 240

2 | 120

2 | 60

2 | 30

5 | 15

3 | 3

1 | 1

Prime Factorisation of 240

= 2 × 2 × 2 × 2 × 5 × 3

Since, 5 and 3 are not in pairs

∴ Smallest Number to be multiplied

= (5 × 3) = 15

∴ Perfect Square

= √(240 × 15) = √(2×2×2×2×15×15)

= √(3,600) = 2 × 2 × 15

= √(3,600) = 60

Hence, the perfect square is 3,600 and the smallest number is 15

√3,600 = 60

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