Which of the following is not equal to $\left[\left(\frac{5}{6}\right)^{\frac{1}{5}}\right]^{-\frac{1}{6}} ?$
$\left(\frac{5}{6}\right)^{\frac{1}{5}-\frac{1}{6}}$
$\frac{1}{\left[\left(\frac{5}{6}\right)^{\frac{1}{5}}\right]^{\frac{1}{6}}}$
$\left(\frac{6}{5}\right)^{\frac{1}{30}}$
$\left(\frac{5}{6}\right)^{-\frac{1}{30}}$
Rationalise the denominator of the following:
$\frac{2}{3 \sqrt{3}}$
Find the value
$\frac{4}{(216)^{-\frac{2}{3}}}+\frac{1}{(256)^{-\frac{3}{4}}}+\frac{2}{(243)^{-\frac{1}{5}}}$
If $a=5+2 \sqrt{6}$ and $b=\frac{1}{a},$ then what will be the value of $a^{2}+b^{2} ?$
Let $x$ and $y$ be rational and irrational numbers, respectively. Is $x+y$ necessarily an irrational number? Give an example in support of your answer.
Find the values of each of the following correct to three places of decimals, rationalising the denominator if needed and taking $\sqrt{2}=1.414$ $\sqrt{3}=1.732$ and $\sqrt{5}=2.236$
$\frac{1}{\sqrt{3}+\sqrt{2}}$