Root 4 of {(17 + 12√ 2 )} =

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Basic of Logarithms

medium

$\root 4 \of {(17 + 12\sqrt 2 )} = $

A

$\sqrt 2 + 1$

B

${2^{1/4}}(\sqrt 2 + 1)$

C

$2\sqrt 2 + 1$

D

None of these

Solution

(a) $\sqrt {(17 + 12\sqrt 2 )} $$ = \sqrt {[{3^2} + {{(2\sqrt 2 )}^2} + 2.3.2\sqrt 2 ]} = 3 + 2\sqrt 2 $

$\therefore \sqrt[4]{{(17 + 12\sqrt 2 )}} = \sqrt {(3 + 2\sqrt 2 )} = \sqrt 2 + 1$

Standard 11

Mathematics

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