Find the square root of 24+2 sqrt{119}. | vedclass

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(C) To find the square root of $24+2 \sqrt{119}$,we assume that $\sqrt{24+2 \sqrt{119}} = \sqrt{x} + \sqrt{y}$.Squaring both sides,we get $24+2 \sqrt{

Vedclass · Accepted Answer

$\sqrt{17}+\sqrt{7}$

Vedclass · Answer

(C) To find the square root of $24+2 \sqrt{119}$,we assume that $\sqrt{24+2 \sqrt{119}} = \sqrt{x} + \sqrt{y}$.Squaring both sides,we get $24+2 \sqrt{119} = x + y + 2 \sqrt{xy}$.Comparing the rational and irrational parts,we have $x + y = 24$ and $xy = 119$.We need two numbers whose sum is $24$ and product is $119$.These numbers are $17$ and $7$,since $17+7=24$ and $17 	imes 7 = 119$.Therefore,$\sqrt{24+2 \sqrt{119}} = \sqrt{17} + \sqrt{7}$.

Find the square root of $24+2 \sqrt{119}$.

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