Problem Solving (PS) | The approximation of 0.8 - 0.1 is between?

\( \sqrt(\frac{8}{10})- \sqrt(\frac{1}{10})\)

\( =\frac{2 \sqrt(3)}{\sqrt(2)\sqrt(5)}-\frac{1}{\sqrt(2)\sqrt(5)}\)

\( =\frac{2\sqrt(3)-1}{\sqrt(2)\sqrt(5)}\)

\( =\frac{\sqrt(2)\sqrt(3) -1}{\sqrt(5)} = \frac{\sqrt(6)-1}{\sqrt(5)}\)

We know\( 2<\sqrt{5}<3\) and also\( 2<\sqrt{6}<3\) Hence\( \sqrt{5} \approx\sqrt{6}\)

Taking\( \sqrt{5} =2\) and\( \sqrt{6} =2\)

\( \frac{\sqrt(6) -1}{\sqrt(5)} = \frac{1}{2}\)

Taking\( \sqrt{5} = 3\) and\( \sqrt{6} =3\)

\( \frac{\sqrt(6) -1}{\sqrt(5)} = \frac{2}{3}\)

Therefore\( \frac{1}{2} < \frac{\sqrt(6) -1}{\sqrt(5)} <\frac{2}{3}\)

Ans D

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