Question

$\sqrt{14 + 6 \sqrt{5} } = \sqrt{x} + \sqrt{y}$
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Answer 1

Answer:

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Step-by-step explanation:

$\sqrt{14 + 6 \sqrt{5} } = \sqrt{x} + \sqrt{y} \\ {( \sqrt{14 + 6 \sqrt{5} } })^{2} = ( { \sqrt{x} + \sqrt{y} }) ^{2} \\ 14 + 6 \sqrt{5} = x + y + 2 \sqrt{xy} \\ so \\ x = 14 \\ y + 2 \sqrt{xy} = 6 \sqrt{5} \\ y + 2 \sqrt{xy} = 4 \sqrt{5} + 2 \sqrt{5} \\ from \: here \\ y = 4 \sqrt{5} \\ and \\ 2\sqrt{14y} = 2 \sqrt{5} \\ 14y = 5 \\ y = \frac{5}{14} \\ so \\ x = 14 \\ y = 4 \sqrt{5} \\ y = \frac{5}{14} \\ anssssssssssssssssssss$