Question

Expand (root 5 + root 3 )4​

Answer 1

SOLUTION

TO DETERMINE

Expand

$\sf{ {( \sqrt{5} + \sqrt{3} )}^{4} }$

EVALUATION

Here we have to expand the expression

$\sf{ {( \sqrt{5} + \sqrt{3} )}^{4} }$

First

$\sf{ {( \sqrt{5} + \sqrt{3} )}^{2} }$

$\sf{ = {{( \sqrt{5} )}^{2} + 2 \times \sqrt{5} \times \sqrt{3} + {(\sqrt{3} )}}^{2} }$

$\sf{ =5 + 2 \sqrt{15} + 3 }$

$\sf{ =8 + 2 \sqrt{15} }$

Now

$\sf{ {( \sqrt{5} + \sqrt{3} )}^{4} }$

$\sf{ = { \bigg( {( \sqrt{5} + \sqrt{3} )}^{2} \bigg)}^{2} }$

$\sf{ = {(8 + 2 \sqrt{15} )}^{2} }$

$\sf{ = {8}^{2} + 2 \times 8 \times 2 \sqrt{15} + {(2 \sqrt{15}) }^{2} }$

$\sf{ = 64+ 32 \sqrt{15} +60 }$

$\sf{ = 124+ 32 \sqrt{15} }$

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