Question

the smallest number that should be subtracted from 300 to make it a perfect square​

Answer 1

11 is the smallest number that should be subtracted from 300 to make it a perfect square

Given :

The number 300

To find :

The smallest number that should be subtracted from 300 to make it a perfect square

Solution :

Step 1 of 2 :

Write down the given number

Here the given number is 300

Step 2 of 2 :

Find the smallest number that should be subtracted from 300 to make it a perfect square

Using long division method we get

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:17\:\:}}}\\ {\underline{\sf{1}}}& {\sf{300}} \\{\sf{}}& \underline{\sf{ \: \: \: \: \: \: \: 1 \: \: \: \: \: \: \: \: \: \: \: \: }} \\ {\underline{\sf{27}}}& {\sf{\: \: \: \: \: \: \: \: 200 \: \: \: \: \: \: \: \: \: }} \\{\sf{}}&\underline{\sf{ \: \: \: \: \: 189 \: \: \: \: \: \: }} \\ {\underline{\sf{}}}&{\sf{\:\: \: 11 \:\:}} {\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

Thus the remainder = 11

If we subtract 11 from 300 then the new number obtained

= 300 - 11

= 289

= 17²

Thus 289 is a perfect square

∴ 11 is the smallest number that should be subtracted from 300 to make it a perfect square

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