Question

Square root of 0.0196 = ?​

Answer 1

$\underline{ \underline{ \Large \pmb{\sf { {Required \: Answer :}} }} }$

✰ Here, we have to find the value of √0.0196 or square root of 0.0196. In order to find the square root of 0.0196, we'll solve it by writing intro fraction then by using the rules of indices we'll find the square root of 0.0196.

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$\longrightarrow \sf { \sqrt{0.0196} = ? }$

We can write this decimal number as fraction,

$\longrightarrow \sf { \sqrt{0.0196} = \sqrt{\dfrac{196}{10000} } }$

Now, as we know that,

$\bigstar \: \boxed{\sf { \sqrt{\dfrac{a}{b} } = \dfrac{\sqrt{a}}{\sqrt{b} } }}$

So, by using this property we can write it as :

$\longrightarrow \sf { \sqrt{0.0196} = \dfrac{\sqrt{196}}{\sqrt{10000}} }$

Now, let's find the square root of 196 and 10000 by prime factorization.

$\star \: \underline{ \sf \red{ Prime \: factorization\: of \: 196}}\\ \\ \begin{array}{c | c} \sf{ \sf \underline{2}}& \sf\underline{196} \\\sf{ \underline{2}} & \sf \underline{98} \\\sf{ \underline{7}}& \sf \underline{49} \\\sf{ \underline{7}} & \sf \underline{7} \\ \: & \sf1\end{array} \\ \\ \star \: \underline{ \sf \red{ Prime \: factorization \: of \: 10000}}\\ \\ \begin{array}{c | c} \sf{ \sf \underline{10}}& \sf\underline{10000} \\\sf{ \underline{10}} & \sf \underline{1000} \\\sf{ \underline{10}}& \sf \underline{100} \\\sf{ \underline{10}} & \sf \underline{10} \\ \: & \sf1\end{array}$

By prime factorization, we get :

$\longrightarrow$ 196 = 2 × 2 × 7 × 7

$\longrightarrow$ √196 = 2 × 7

$\longrightarrow$ √196 = 14

Also,

$\longrightarrow$ 10000 = 10 × 10 × 10 × 10

$\longrightarrow$ √10000 = 10 × 10

$\longrightarrow$ √10000 = 100

So,

$\longrightarrow \sf { \sqrt{0.0196} = \dfrac{14}{100} }$

Writing the fraction in decimal.

$\longrightarrow \boxed{ \pmb{\rm \red {{ \sqrt{0.0196} = 0.14} }} }$

Therefore, square root of 0.0196 is 0.14.