Question

√0.85 (0.105 +0.024 -0.008)/
0.022 x 0.25 X 1.7
Simplified​

Answer 1

Step-by-step explanation:

$\bf \underline{Simplify-}$

${\sf \: \: \: \sqrt{ \dfrac{ 0.85×(0.105+0.024-0.008)}{0.022×0.25×1.7}} }$

$\bf \underline{Solution-}$

${ \: \: \: \: \sqrt{ \dfrac{ 0.85×(0.105+0.024-0.008)}{0.022×0.25×1.7}}}$

${ \: \: \: \: \: \implies\sqrt{ \dfrac{ \dfrac{85}{100} \times \left( \dfrac{105}{1000} + \dfrac{24}{1000} - \dfrac{8}{1000} \right)}{ \dfrac{22}{1000} × \dfrac{25}{100} × \dfrac{17}{10} }}}$

${\implies\sqrt{ \dfrac{ \dfrac{85}{100} \times \left( \dfrac{105 + 24 - 8}{1000} \right)}{ \dfrac{22 \times 25 \times 17}{1000 \times 100 \times 10} }}}$

${\implies\sqrt{ \dfrac{ \dfrac{85}{100} \times \dfrac{121}{1000} }{ \dfrac{9350}{1000000} }}}$

${~~~~~~~~~\implies\sqrt{ \dfrac{ \dfrac{10285}{100000} }{ \dfrac{9350}{1000000} }}}$

${~~~~~~~\implies\sqrt{\dfrac{ \cancel{10285}^{935} }{ \cancel{100000}^{1} } \times \dfrac{ \cancel{100000}^{1} \: \: \times 10}{ \cancel{9350} ^{850} } }}$

${~~~~~~~~~~~~~~\implies\sqrt{ \dfrac{ \cancel{9350}^{11} }{ \cancel{850}} }}$

${~~~~~~~~~~~~~~~\implies\sqrt{ 11 }}$

$\rm{{\boxed{Hence, the \: value \: of \: { \sqrt{ \dfrac{ 0.85×(0.105+0.024-0.008)}{0.022×0.25×1.7} } \: is \: \sqrt{11}} }}}$