Question

Page No: 5
LP
Date:...1.1.
solve the following
find out the smallest number which when
multiplied by 200, so that the product
becomes
perfect square,
​

Answer 1

Answer:

Solution :-

To find the least number by which 200 must be multiplied so that the product becomes a perfect square, we have to find of the prime factors of 200.

Prime Factorization of 200 = 2 × 2 × 2 × 5 × 5

By grouping the factors in pair of two [(2*2 and 5*5)*2 = 200], we observe that a 2 is without pair.

Thus, we must multiply 200 by 2, so that the product becomes a perfect square.

⇒ 200 × 2 = 400

400 is a square of 20.

So, the least number is 2, by which 200 must be multiplied so that the product becomes a perfect square.

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