Question

What least number should be subtracted from 49299 to make it perfect square by division method. ( Show the steps)​

Answer 1

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

Given number is 49299

Using long division, we have

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:222 \:\:}}}\\ {\underline{\sf{2}}}& {\sf{\:\:49299 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \:4 \: \: \:  \:  \:  \:  \:  }} \\ {\underline{\sf{42}}}& {\sf{\:\: \: \: \: \: 92 \: \: \: \: \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \:84 \: \:   \:  \: \:\:}} \\ {\underline{\sf{442}}}& {\sf{\: \: \: \: \: \: \:899  \:\:}} \\{\sf{}}& \underline{\sf{\: \: \: \: \: \:884\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \:  \:  \:  15 \: \: \: \:\:}} {\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

$\rm :\implies\:15 \: must \: be \: subtracted \: to \: get \: a \: perfect \: square.$

Thus,

$\rm :\longmapsto\:Number \: = 49299 - 15 = 49284$

and

$\rm :\longmapsto\: \sqrt{49284} = 222$

Additional information :-

Let us consider one more example.

Example :- What least number should be added to 49299 to make it perfect square by division method.

Solution :-

Using long division method

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:223 \:\:}}}\\ {\underline{\sf{2}}}& {\sf{\:\:49299 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \:4 \: \: \:  \:  \:  \:  \:  }} \\ {\underline{\sf{42}}}& {\sf{\:\: \: \: \: \: 92 \: \: \: \: \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \:84 \: \:   \:  \: \:\:}} \\ {\underline{\sf{443}}}& {\sf{\: \: \: \: \: \: \:899  \:\:}} \\{\sf{}}& \underline{\sf{\: \: \: \: \: \:1329\: \: \: \:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \:  \:  \:  - 430 \: \: \: \: \: \: \: \: \: \: \:\:}} {\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

$\rm :\implies\:430 \: must \: be \: added \: to \: get \: a \: perfect \: square.$

Thus,

$\rm :\longmapsto\:Number \: = 49299 + 430 = 49729$

And

$\rm :\longmapsto\: \sqrt{49729} = 223$