Question

What is the smallest positive number that should be added to 2525 so that the square root of the resultant sum is a natural number? ​

Answer 1

Answer:

(51)2

2601

2601-2525

76

Answer 2

$\fbox{ QUESTION }$

What is the smallest positive number that should be added to 2525 so that the square root of the resultant sum is a natural number? ​

$\fbox{ ANSWER }$

step 1 :

Separate the digits by taking commas from right to left once in two digits.

19, 89

When we do so, we get 19 before the comma.

Step 2 :

Now we have to multiply a number by itself such that the product ≤ 4

(The product must be greatest and also less than 19)

The above condition will be met by “4”.

Because 4 ⋅ 4  =  16

Now this situation is explained using long division

In the above picture, 16 is subtracted from 19 and we got the remainder 3.

Step 3 :

Now, we have to bring down 89 and quotient 4 to be multiplied by 2. So we get 8.

By multiplying 4 and 84 we get 336.

If we subtract 336 from 389, we get 53.

We don't have to continue hereafter.

44 (44)  =  1936

If we subtract 53 from 1989, we get 1936 which is the perfect square.

Hence 53 is the least number to be subtracted from the given number (1989) to get a perfect square.