Question

Find the value of √3136 and use it to find the value of √31.36 + √0.3136

Answer 1

$\textbf{To find:}$

$\text{The value of \sqrt{31.36}+\sqrt{0.3136} }$

$\textbf{Solution:}$

$\text{First we find the square root of 3136}$

$\begin{array}{r|l}2&3136\\\cline{2-2}2&1568\\\cline{2-2}2&784\\\cline{2-2}2&392\\\cline{2-2}2&196\\\cline{2-2}2&98\\\cline{2-2}7&49\\\cline{2-2}7&7\\\cline{2-2}&1\\\cline{2-2}\end{array}$

$3136=2^2{\times}2^2{\times}2^2{\times}7^2$

$\sqrt{3136}=2{\times}2{\times}2{\times}7$

$\implies\bf\sqrt{3136}=56$

$\text{Now,}$

$\sqrt{31.36}+\sqrt{0.3136}$

$=\sqrt{\dfrac{3136}{100}}+\sqrt{\dfrac{3136}{10000}}$

$=\dfrac{\sqrt{3136}}{\sqrt{100}}+\dfrac{\sqrt{3136}}{\sqrt{10000}}$

$=\dfrac{56}{10}+\dfrac{56}{100}$

$=5.6+0.56$

$=6.16$

$\therefore\textbf{The value of \bf\,\sqrt{31.36}+\sqrt{0.3136} is 6.16}$

Find more:

How to find the square root of 306.25

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Answer 2

hope it helps u,bro. all the best