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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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: $3 - \frac{1}{3} \sqrt{56}$

Similar Questions

The numbers $525$ and $3000$ are both divisible by $3, 5, 15, 25,$ and $75$. What is $HCF(525, 3000)$? Justify your answer.

The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after

If $\text{g.c.d.}(336, 52) = 4$,then $\text{l.c.m.}(336, 52) = \dots$

The smallest positive number greater than $5$ such that when it is divided by $20, 30,$ or $40,$ it leaves the remainder $5$ is:

$\sqrt{8+4 \sqrt{3}} = \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module