Question

Find the least number that must be subtracted from 3129 to make it a perfect square.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given number is 3129.

Since, we have to find the least number that must be subtracted  to 3129 to make it a perfect square.

So, we use long division to find the remainder that should be subtracted  to the given number to make it a perfect square.

Thus,

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:55 \:\:}}}\\ {\underline{\sf{5}}}& {\sf{\:\:3129 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: 25  \: \: \: \: \: \:}} \\ {\underline{\sf{105}}}& {\sf{\:\: \: \: \: \: 629 \:  \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: 525   \:}} \\ {\underline{\sf{}}}& {\sf{ \: \: \:\:104  \:\:}} {\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

So, it means 104 must be subtracted  to 3129 to make it a perfect square.

Thus, Required number is 3129 - 104 = 3025.

So,

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:55 \:\:}}}\\ {\underline{\sf{5}}}& {\sf{\:\:3025 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: 25  \: \: \: \: \: \:}} \\ {\underline{\sf{105}}}& {\sf{\:\: \: \: \: \: 525 \:  \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: 525   \:}} \\ {\underline{\sf{}}}& {\sf{ \: \: \:\:00  \:\:}} {\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

Thus,

$\rm \implies\:\boxed{ \tt{ \: \: \sqrt{3025} \: \: = \: \: 55 \: \: }}$