Question

Find out the least number which when divided by 200 will make a quotient a perfect square​

Answer 1

ANSWER

HI MATE HERE IS THE ANSWER

STEP BY STEP EXPLANATION:

Hint: A perfect square is a number which has all its prime factors in pairs. We will divide 200 by the smallest prime number. We will use the same approach to calculate it further. A prime factor is a factor of the given number which is a prime number also.

Complete step by step answer:

(1) Given number is200

Making prime factors of200

.

Or 200=2×2×2×5×5

(2) Writing in pair

200=2×2×5×5×2

(3) In the above step, we see that there is only one number 2 which does not have its pair. We can see that other numbers such as 5 and other 2 have pairs.

Therefore, we can say that 200

is not a perfect square number.

(4) Now to make 200

, a perfect square number, we need to multiply 200 in such a manner that it completes its pair which is not other than 2.

(5) Therefore by multiplying 200

by 2, we get the following prime factors 2×2×5×5×2×2

(6) We see all the prime factors 200

are now in pairs.

Therefore, multiplying 200

by 2,200

becomes 400 is a perfect square.

(7) Therefore, the least number we require to make 200

a perfect square is 2. The perfect square is 400.

Note: A square number or perfect square is an integer that is a square of an integer; in other words, it is the product of some integer with itself. Taking the square root of a perfect square always gives us an integer

Answer 2

Given:

To find out the least number which when divided by 200 will make a quotient a perfect square​.

Solution:

Understand that To find out the least number, the quotient should  also be least and perfect square.

Know that the smallest perfect square number is 4,

Let the smallest number which when divided by 200 will make a quotient a perfect square​ is $x$,

$\[\begin{array}{l} \Rightarrow \frac{x}{{200}} = 4\\ \Rightarrow x = 800\end{array}\]$

Hence the least number which when divided by 200 will make a quotient a perfect square​ is 800.