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

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1. [tex]\large\underline{\sf{Solution-}}[/tex]

   Given number is 49299

   Using long division, we have

   [tex]\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}[/tex]

   [tex]\rm :\implies\:15 \: must \: be \: subtracted \: to \: get \: a \: perfect \: square.[/tex]

   Thus,

   [tex]\rm :\longmapsto\:Number \: = 49299 – 15 = 49284[/tex]

   and

   [tex]\rm :\longmapsto\: \sqrt{49284} = 222 [/tex]

   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

   [tex]\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}[/tex]

   [tex]\rm :\implies\:430 \: must \: be \: added \: to \: get \: a \: perfect \: square.[/tex]

   Thus,

   [tex]\rm :\longmapsto\:Number \: = 49299 + 430 = 49729[/tex]

   And

   [tex]\rm :\longmapsto\: \sqrt{49729} = 223 [/tex]

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