Find the square root of the expression 55-14 | vedclass

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Question

(A) To find the square root of $55-14 \sqrt{6}$,we assume it is of the form $(a-b)^2 = a^2 + b^2 - 2ab$.We can rewrite the expression as $55 - 2 	ime

Vedclass · Accepted Answer

$7-\sqrt{6}$

Vedclass · Answer

(A) To find the square root of $55-14 \sqrt{6}$,we assume it is of the form $(a-b)^2 = a^2 + b^2 - 2ab$.We can rewrite the expression as $55 - 2 	imes 7 	imes \sqrt{6} 	imes \sqrt{1}$.Let $a = 7$ and $b = \sqrt{6}$.Then $a^2 + b^2 = 7^2 + (\sqrt{6})^2 = 49 + 6 = 55$.This matches the given expression.Therefore,$55 - 14 \sqrt{6} = 7^2 + (\sqrt{6})^2 - 2(7)(\sqrt{6}) = (7-\sqrt{6})^2$.The square root is $\sqrt{(7-\sqrt{6})^2} = 7-\sqrt{6}$.

Find the square root of the expression $55-14 \sqrt{6}$ in the form of a binomial surd.

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