sqrt{12-sqrt{140}} = dots | vedclass

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Question

(C) To simplify the expression $\sqrt{12-\sqrt{140}}$,we first rewrite $\sqrt{140}$ as $2\sqrt{35}$.Thus,the expression becomes $\sqrt{12-2\sqrt{35}}$

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) To simplify the expression $\sqrt{12-\sqrt{140}}$,we first rewrite $\sqrt{140}$ as $2\sqrt{35}$.Thus,the expression becomes $\sqrt{12-2\sqrt{35}}$.We look for two numbers whose sum is $12$ and whose product is $35$. These numbers are $7$ and $5$.We can write $12$ as $(7+5)$ and $35$ as $(7 	imes 5)$.So,$\sqrt{12-2\sqrt{35}} = \sqrt{(7+5)-2\sqrt{7 	imes 5}}$.Using the identity $(a-b)^2 = a^2+b^2-2ab$,we have $\sqrt{(\sqrt{7}-\sqrt{5})^2}$.Therefore,the result is $\sqrt{7}-\sqrt{5}$.

$\sqrt{12-\sqrt{140}} = \dots$

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