AP ICET 2017 Shift 1 Paper

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Question : 80 of 200

Marks: +1, -0

Taking

√{5}=2.2360

the value of

\;\;{√{3-√{5}}}/{√{2}+√{7-3√{5}}}=

$0.4247$
$0.4472$
$0.4274$
$0.4742$

Solution:

√{3-√{5}}=√{{6-2√{5}}/{2}}=√{{(√{5}-1)^{2}}/{2}}={√{5}-1}/{√{2}}

√{7-3√{5}}=√{{14-6√{5}}/{2}}=√{{(3-√{5})^{2}}/{2}}={3-√{5}}/{√{2}}

∴{√{3-√{5}}}/{√{2}+√{7-3√{5}}}={(√{5}-1)/√{2}}/{√{2}+(3√{5})/√{2}}

={√{5}-1}/{2+3-√{5}}={√{5}-1}/{5-√{5}}={(√{5}-1)}/{√{5}(√{5-1})}

={1}/{√{5}}={√{5}}/{5}={2.2360}/{5}=0.4472

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