The value of frac{1+sqrt{0.01}}{1-sqrt{0.1}} | vedclass

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Question

(C) Given expression is $\frac{1+\sqrt{0.01}}{1-\sqrt{0.1}}$.Since $\sqrt{0.01} = 0.1$,the expression becomes $\frac{1+0.1}{1-\sqrt{0.1}} = \frac{1.1}

Vedclass · Accepted Answer

$1.6$

Vedclass · Answer

(C) Given expression is $\frac{1+\sqrt{0.01}}{1-\sqrt{0.1}}$.Since $\sqrt{0.01} = 0.1$,the expression becomes $\frac{1+0.1}{1-\sqrt{0.1}} = \frac{1.1}{1-\sqrt{0.1}}$.To rationalize the denominator,multiply the numerator and denominator by $(1+\sqrt{0.1})$:$\frac{1.1(1+\sqrt{0.1})}{(1-\sqrt{0.1})(1+\sqrt{0.1})} = \frac{1.1(1+\sqrt{0.1})}{1-0.1} = \frac{1.1(1+\sqrt{0.1})}{0.9}$.Using the approximation $\sqrt{0.1} \approx 0.3162$:$= \frac{1.1(1+0.3162)}{0.9} = \frac{1.1(1.3162)}{0.9} = \frac{1.44782}{0.9} \approx 1.6086$.Rounding to one decimal place,the value is approximately $1.6$.

The value of $\frac{1+\sqrt{0.01}}{1-\sqrt{0.1}}$ is nearly equal to

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