Question 1

What least number can be multiplied by 165375 to make it a perfect cube?

Solution

Prime factorisation of $$165375 = 3^3\times5^3\times7^2$$

Now, the exponents of 3 and 5 are divisible by 3 (for perfect cube) and we need one more '7' so that exponent of 7 can also get divisible by 3.

=> 165375 should be multiplied by 7 to make it a perfect cube.

=> Ans - (C)

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