Question

Find the smallest whole no. By which 1000 should be multiplied to make it a perfect square also find the square root of the new number.

Answer 1

1000 should be subjected to prime factorization to get the following:

1000 = 2³ × 5³

Here the exponents are odd, when they become even, then the number will be a perfect square.

2³ in here should be multiplied with 2 to get 2⁴.

Also, 5³ should be multiplied with 5 to get 5⁴.

∴ 2³ × 5³ should be multiplied with 2 × 5 = 10 to be a perfect square.

So 10 is the answer.

Let's find the square root of the new number.

New number is 2⁴ × 5⁴ = 10000.

Square roots of 10000 are 100 and -100.

So the answer is ±100.

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