If we have a square root as $\sqrt{1.21} = 1.1$ , then $\sqrt{. 000121}$ is equal to:

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0.0011

0.011

0.11

11.0

answer is B.

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Detailed Solution

Concept- Divide by 10 and multiply by 10 inside the square root. Just simplify the numerator and denominator separately, until we get the value of the number for which we already know the square root.
Given:

\sqrt{1.21} = 1.1

\sqrt{0.000121} = ?

We will have to convert this number into the form of 1.21.
On multiplying and dividing with 10, to the number:-

\Rightarrow \frac{0.000121 \times}{10} 10 = \frac{0.00121}{10}

On multiplying and dividing with 10 to above number:-

\Rightarrow \frac{0.00121}{10} \times \frac{10}{10} = \frac{0.0121}{10^{2}}

On multiplying and dividing with 10 again:-

\Rightarrow \frac{1.21}{10^{4}} = 0.000121

On applying square root on both sides:-

\Rightarrow \sqrt{0.000121} = \sqrt{\frac{1.21}{10^{4}}}

\Rightarrow \sqrt{\frac{1.21}{10^{4}}} = \frac{\sqrt{1.21}}{\sqrt{10^{4}}}

On simplifying and substituting the value, we get

\Rightarrow \frac{1.1}{10^{2}} \Rightarrow 0.011

Hence,

\sqrt{0.000121} = 0.011

Hence, option (2) is the correct answer.

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