Question

kindly give step by step explanation​

Answer 1

Step-by-step explanation:

(0.0196)^1/2=(196/10000)^1/2=(14/100)^2×1/2=14/100

=0.14

please Subscribe my yt channel JK Tutorial 1M It is an educational channel for cbse students

Answer 2

Given Question :-

Evaluate

$\rm :\longmapsto\: \sqrt{0.0196}$

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

Given square root is

$\rm :\longmapsto\: \sqrt{0.0196}$

$\rm \: = \: \sqrt{\dfrac{196}{10000} }$

Let first find prime factors of 196,

$\purple{\rm :\longmapsto\:Prime \: factorization \: of \: 196 \: }$

$\purple{\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:196 \:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:98 \:\:}} \\\underline{\sf{7}}&\underline{\sf{\:\:49\:\:}} \\ {\underline{\sf{7}}}& \underline{\sf{\:\:7\:\:}}\\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}}$

Thus,

$\purple{\rm :\longmapsto\:Prime \: factorization \: of \: 196 \: = 2 \times 2 \times 7 \times 7}$

Thus,

$\rm \: = \: \sqrt{\dfrac{2 \times 2 \times 7 \times 7}{10 \times 10 \times 10 \times 10} }$

$\rm \: = \:\dfrac{2 \times 7}{10 \times 10}$

$\rm \: = \:\dfrac{14}{100}$

$\rm \: = \:0.14$

$\green{\bf\implies \:\boxed{ \tt{ \: \sqrt{0.0196} = 0.14 \: }}}$

Alternative Method :-

Given square root is

$\rm :\longmapsto\: \sqrt{0.0196}$

Using Long Division Method, we have

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:0.14 \:\:}}}\\ {\underline{\sf{1}}}& {\sf{\:\:0.0196 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: \: 1 \:  \:  \:  \:\:}} \\ {\underline{\sf{24}}}& {\sf{\:\: \: \: \: \: \: \: \: \: 96 \: \:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: 96}} \\ {\underline{\sf{}}}& {\sf{\: \:  \:  \:  \:  \:\: 0\:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

$\red{\bf\implies \:\boxed{ \tt{ \: \sqrt{0.0196} = 0.14 \: }}}$