Question

find the least no. by which 135000 should be divided to make it a perfect square

Answer 1

Heya !!!

This is your answer.....

Given :-- 135000.
We have to find smallest number by which it should be divided to make it a perfect square....

So...First

Prime factors of 135000 ......
135000 = 2×2×2×3×3×3×5×5×5×5.

We can see that two factors i.e. 2 and 3 are unpaired. If we remove them by dividing them by 2 and 3... then the factors left will be in pair..... and form a perfect square.
Hence ...

135000 × 1/2× 1/3 = 2×2×2×1/2×3×3×3×1/3×5×5×5×5.

Hence the new number formed will be a perfect square.....

So.. the smallest number by which it should be divided is 2×3= 6.

Hope it helpssss