Question

Find the smallest number which when subtracted from 13250 changes it to a perfect square.

Answer 1

Step-by-step explanation:

$\huge\mathfrak\green{ so \:your\: answer\: is}$

First, we have to find the squares of 11 and 13 and add them up.

Square of 11 = 121 ( 11 * 11 )

Square of 13 = 169 ( 13 * 13 )

On adding these numbers, we get :-

= 121 + 169

= 290

Now, Since we have to find the smallest number which when subtracted from 290 gives us a perfect square, we will find all the perfect squares near 290.

Now, the squares of 17 and 18 are the closest.

Square of 17 = 289 ( 17 * 17 )

Square of 18 = 324 ( 18 * 18 )

We can clearly see that 289 is the closest perfect square to 290.

Now, we have to find the number which when subtracted from 290 will give 289.

Let us take this number to be "x". Then,

=> 290 - x = 289

=> 290 - 289 = x

=> x = 1

Therefore, the smallest number which when subtracted from the sum of squares of 11 and 13 gives a perfect square is 1.

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Answer 2

If we subtract 25 from 13250 then it becomes a perfect square so,

13250- 25 = 13225

√13225 = 115

Hope this helps you