If $a=2+\sqrt{3}$, then find the value of $a-\frac{1}{a}$.

Rationalize the denominator and hence evaluate by taking $\sqrt{2}=1.414,\sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three places of decimal.

$\frac{4}{\sqrt{3}}$

Rationalize the denominator and hence evaluate by taking $\sqrt{2}=1.414,\sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three places of decimal.

$\frac{6}{\sqrt{6}}$

Rationalize the denominator and hence evaluate by taking $\sqrt{2}=1.414,\sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three places of decimal.

$\frac{\sqrt{10}-\sqrt{5}}{2}$

Rationalize the denominator and hence evaluate by taking $\sqrt{2}=1.414,\sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three places of decimal.

$\frac{\sqrt{2}}{2+\sqrt{2}}$ 

Rationalize the denominator and hence evaluate by taking $\sqrt{2}=1.414,\sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three places of decimal.

$\frac{1}{\sqrt{3}+\sqrt{2}}$

Simplify the following:
${\left(1^3+2^3+3^3\right)}^{\frac{1}{2}}$

Simplify the following:
${\left(\frac{3}{5}\right)}^4{\left(\frac{8}{5}\right)}^{-12}{\left(\frac{32}{5}\right)}^6$

Simplify the following:
${\left(\frac{1}{27}\right)}^{\frac{-2}{3}}$