Find the square root of 12-sqrt{140}. | vedclass

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(D) To find the square root of $12-\sqrt{140}$,we can write it in the form $\sqrt{a-b}$.First,simplify $\sqrt{140}$ as $\sqrt{4 	imes 35} = 2\sqrt{35

Vedclass · Accepted Answer

$\sqrt{7}-\sqrt{5}$

Vedclass · Answer

(D) To find the square root of $12-\sqrt{140}$,we can write it in the form $\sqrt{a-b}$.First,simplify $\sqrt{140}$ as $\sqrt{4 	imes 35} = 2\sqrt{35}$.So,the expression becomes $12 - 2\sqrt{35}$.We want to express this in the form $(\sqrt{x} - \sqrt{y})^2 = x + y - 2\sqrt{xy}$.Comparing $x + y = 12$ and $2\sqrt{xy} = 2\sqrt{35}$,we get $xy = 35$.The factors of $35$ that add up to $12$ are $7$ and $5$.Thus,$12 - 2\sqrt{35} = 7 + 5 - 2\sqrt{7 	imes 5} = (\sqrt{7})^2 + (\sqrt{5})^2 - 2\sqrt{7}\sqrt{5} = (\sqrt{7} - \sqrt{5})^2$.Therefore,the square root is $\sqrt{(\sqrt{7} - \sqrt{5})^2} = \sqrt{7} - \sqrt{5}$.

Find the square root of $12-\sqrt{140}$.

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