Question

Find the smallest number by which 500 must be multiplied so that it becomes a parfect square.Also , find the square root of the number so obtained.​

Answer 1

Answer:

Correct option is

D

2

Prime factorising 500, we get,

500=5×5×5×2×2

=5

3

×2

2

.

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 2's is 2 and number of 5's is 3.

So we need to multiply another 2 to the factorization to make 500 a perfect cube.

Hence, the smallest number by which 500 must be multiplied to obtain a perfect cube is 2.

Therefore, option D is correct.

Answer 2

Prime factorising 500, we get,

500=5×5×5×2×2

=5

3

×2

2

.

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 2's is 2 and number of 5's is 3.

So we need to multiply another 2 to the factorization to make 500 a perfect cube.

Hence, the smallest number by which 500 must be multiplied to obtain a perfect cube is 2.