The square root of 134 + sqrt{6292} is: | vedclass

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(B) We need to find the square root of $134 + \sqrt{6292}$.First,simplify $\sqrt{6292} = \sqrt{4 	imes 1573} = 2\sqrt{1573}$.So,the expression is $13

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$11 + \sqrt{13}$

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(B) We need to find the square root of $134 + \sqrt{6292}$.First,simplify $\sqrt{6292} = \sqrt{4 	imes 1573} = 2\sqrt{1573}$.So,the expression is $134 + 2\sqrt{1573}$.We want to express this in the form $(\sqrt{x} + \sqrt{y})^2 = x + y + 2\sqrt{xy}$.Comparing,$x + y = 134$ and $xy = 1573$.The quadratic equation $t^2 - 134t + 1573 = 0$ has roots $t = \frac{134 \pm \sqrt{134^2 - 4(1573)}}{2}$.$134^2 = 17956$ and $4 	imes 1573 = 6292$.$17956 - 6292 = 11664$,and $\sqrt{11664} = 108$.So,$t = \frac{134 \pm 108}{2}$.$t_1 = \frac{242}{2} = 121$ and $t_2 = \frac{26}{2} = 13$.Thus,$134 + 2\sqrt{1573} = (\sqrt{121} + \sqrt{13})^2 = (11 + \sqrt{13})^2$.The square root is $11 + \sqrt{13}$.

The square root of $134 + \sqrt{6292}$ is:

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