Question

Evaluate 15÷(/sqrt{10}+/sqrt{20}+/sqrt{40}-/sqrt{5}-/sqrt{80} ) given that /sqrt{5}=2.236 and /sqrt{10} = 3.162

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Answer 1

$\huge{ \underline{ \mathfrak{ \green{ \: Answer}}}}$

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$\boxed{\red{\bold{Convert \: all \: to \: factors \: of\: \sqrt{5} \:or\:\sqrt{10}:}}}$

$\implies$${\displaystyle{\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}}}$

$\implies$${\displaystyle{\frac{15}{\sqrt{10} + \sqrt{5 × 4} + \sqrt{4 × 10} - \sqrt{5} - \sqrt{16 × 5}}}}$

$\implies$${\displaystyle{\frac{15}{\sqrt{10} + 2\sqrt{5} + 2\sqrt{10} - \sqrt{5} - 4\sqrt{5}}}}$

$\boxed{\red{\bold{Now\:put\:values\:of\:\sqrt{10} \: and \: \sqrt{5}:}}}$

$\implies$$\displaystyle{\frac{15}{3.162 + 2 × 2.236 + 2 × 3.162 - 2.236 - 4 × 2.236}}$

$\implies$$\displaystyle{\frac{15}{3.162 + 4.472 + 6.324 - 2.236 - 8.944}}$

$\implies$$\displaystyle{\frac{15}{2.778}}$

$\implies$$\displaystyle{\frac{15 × 1000}{2778}}$

$\implies$$\displaystyle{\frac{5 × 1000}{926}}$

$\blue{\bold{\underline{Hence \: the\: answer\: is \: 5.3995680346(approx)}}}$

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