Question

find the smallest number which must be subtracted from each of the following to get a perfect square also writers their root of the number so obtained number is 18 268

Answer 1

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

Given number is 18268

Since, we have to find the smallest number which must be subtracted from 18268 to get a perfect square.

So, we have to perform Long Division Method to find the smallest number which must be subtracted from 18268 to get a perfect square.

So, using Long Division Method, we have

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:135 \:\:}}}\\ {\underline{\sf{1}}}& {\sf{\:\:18268 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: 1 \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{23}}}& {\sf{\:\: 82 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: 69 \:  \:}} \\ {\underline{\sf{265}}}& {\sf{\: \: \: \: \: \: \: \:1368 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: 1325\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \: \: \: \: \: \: \: 43\:\:}} \end{array}\end{gathered}\end{gathered}$

So, it means 43 must be subtracted from 18268 to get a perfect square.

So, required number = 18268 - 43 = 18225

So,

$\red{\rm :\longmapsto\: \sqrt{18225}}$

Using Long Division Method, we have

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:135 \:\:}}}\\ {\underline{\sf{1}}}& {\sf{\:\:18225 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: 1 \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{23}}}& {\sf{\:\: 82 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: 69 \:  \:}} \\ {\underline{\sf{265}}}& {\sf{\: \: \: \: \: \: \: \:1325 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: 1325\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \: \: \: \: \: \: \: 0\:\:}} \end{array}\end{gathered}\end{gathered}$

Hence,

$\rm \implies\:\boxed{\tt{ \: \sqrt{18225} = 135 \: }}$

Answer 2

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

Given number is 18268

Since, we have to find the smallest number which must be subtracted from 18268 to get a perfect square.

So, we have to perform Long Division Method to find the smallest number which must be subtracted from 18268 to get a perfect square.

So, using Long Division Method, we have

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:135 \:\:}}}\\ {\underline{\sf{1}}}& {\sf{\:\:18268 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: 1 \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{23}}}& {\sf{\:\: 82 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: 69 \:  \:}} \\ {\underline{\sf{265}}}& {\sf{\: \: \: \: \: \: \: \:1368 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: 1325\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \: \: \: \: \: \: \: 43\:\:}} \end{array}\end{gathered}\end{gathered}$

So, it means 43 must be subtracted from 18268 to get a perfect square.

So, required number = 18268 - 43 = 18225

So,

$\red{\rm :\longmapsto\: \sqrt{18225}}$

Using Long Division Method, we have

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:135 \:\:}}}\\ {\underline{\sf{1}}}& {\sf{\:\:18225 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: 1 \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{23}}}& {\sf{\:\: 82 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: 69 \:  \:}} \\ {\underline{\sf{265}}}& {\sf{\: \: \: \: \: \: \: \:1325 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: 1325\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \: \: \: \: \: \: \: 0\:\:}} \end{array}\end{gathered}\end{gathered}$

Hence,

$\rm \implies\:\boxed{\tt{ \: \sqrt{18225} = 135 \: }}$