Question

Find the value of √116281 and evaluate √1162.81+√11.6281

Answer 1

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

Consider,

$\rm :\longmapsto\: \sqrt{116281}$

Let's evaluate this square root by Long Division Method.

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:341 \:\:}}}\\ {\underline{\sf{3}}}& {\sf{\:\:116281 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: \: 9 \:  \:  \:  \:    \:  \:  \: \:\:}} \\ {\underline{\sf{64}}}& {\sf{\:\: \: \: \: \: 262 \:  \: \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: 256 \:  \: \: \: \:\:}} \\ {\underline{\sf{681}}}& {\sf{\: \: \: \: \: \: \: \: \:681  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: 681\:\:}} \\ {\underline{\sf{}}}& {\sf{\: \:  \:  \: \: 0\:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

Hence,

$\rm :\longmapsto\: \sqrt{116281} = 341$

Now, Consider

$\red{\rm :\longmapsto\: \sqrt{1162.81} }$

$\red{\rm \: = \: \sqrt{\dfrac{116281}{100} }}$

$\red{\rm \: = \:\dfrac{ \sqrt{116281} }{ \sqrt{100} }}$

$\red{\rm \: = \:\dfrac{341}{10}}$

$\red{\rm \: = \:34.1}$

$\red{\bf\implies \: \sqrt{1162.81} \: = \:34.1}$

Now, Consider

$\green{\rm :\longmapsto\: \sqrt{11.6281} }$

$\green{\rm \: = \: \sqrt{\dfrac{116281}{10000} }}$

$\green{\rm \: = \:\dfrac{ \sqrt{116281} }{ \sqrt{10000} }}$

$\green{\rm \: = \:\dfrac{341}{100}}$

$\green{\rm \: = \:3.41}$

$\green{\bf\implies \: \sqrt{11.6281} \: = \:3.41}$

Now, Consider

$\purple{\rm :\longmapsto\: \sqrt{1162.81} + \sqrt{11.6281}}$

$\purple{\rm \: = \:34.1 + 3.41}$

$\purple{\rm \: = \:37.51}$

Hence,

$\purple{\bf\implies \: \sqrt{1162.81} + \sqrt{11.6281} = 37.51}$

Answer 2

Answer:

$Hence, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \\ </p><p></p><p>\purple{\bf\implies \: \sqrt{1162.81} + \sqrt{11.6281} = 37.51}$