Find the square root of: 3 - frac{1}{3} sqrt{ | vedclass

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Question

(A) We need to find $\sqrt{3 - \frac{1}{3} \sqrt{56}}$.First,rewrite the expression: $\sqrt{3 - \frac{\sqrt{56}}{3}} = \sqrt{\frac{9 - \sqrt{56}}{3}}

Vedclass · Accepted Answer

$\sqrt{\frac{7}{3}} - \sqrt{\frac{2}{3}}$

Vedclass · Answer

(A) We need to find $\sqrt{3 - \frac{1}{3} \sqrt{56}}$.First,rewrite the expression: $\sqrt{3 - \frac{\sqrt{56}}{3}} = \sqrt{\frac{9 - \sqrt{56}}{3}} = \sqrt{\frac{9 - 2\sqrt{14}}{3}}$.To simplify $\sqrt{9 - 2\sqrt{14}}$,we look for two numbers $a$ and $b$ such that $a+b=9$ and $ab=14$. These numbers are $7$ and $2$.So,$\sqrt{9 - 2\sqrt{14}} = \sqrt{7} - \sqrt{2}$.Thus,the expression becomes $\frac{\sqrt{7} - \sqrt{2}}{\sqrt{3}} = \sqrt{\frac{7}{3}} - \sqrt{\frac{2}{3}}$.

Find the square root of: $3 - \frac{1}{3} \sqrt{56}$

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