Question

Simplify(using Identitiy)
$( \sqrt[5]{5 } + \sqrt[7]{3} )( \sqrt[5]{5} + \sqrt[7]{3} )$
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Answer 1

Step-by-step explanation:

$(5 \sqrt{5} + 7 \sqrt{3} )(5 \sqrt{5} + 7 \sqrt{3} )$

$= ( {5 \sqrt{5} + 7\sqrt{3} )}^{2}$

$= ( {5 \sqrt{5} )}^{2} + 2 \times 5 \sqrt{5} \times 7 \sqrt{3} + ( {7 \sqrt{3} )}^{2}$

$= 25 \times 5 + 70 \sqrt{15} + 49 \times 3$

$= 125 + 70 \sqrt{15} + 147$

$= 272 + 70 \sqrt{15}$