find the least number by which 200 must be multiplied so that their product is a perfect square
Answers
Answered by
6
2 is the least number
Answered by
36
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.
Answer.
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.
Answer.
Similar questions