Surds and Indices

Arrange $\sqrt[4]{3} ,\sqrt[6]{10 },\sqrt[12]{25}$ in descending order.

$$2+\cfrac { 6 }{ \sqrt { 3 } } +\cfrac { 1 }{ 2+\sqrt { 3 } } +\cfrac { 1 }{ \sqrt { 3 } -2 } =?$$

Arrange the following in descending order:

$\sqrt[3]{4}, \sqrt{2}, \sqrt[6]{3}, \sqrt[4]{5}$

If $x=1+\sqrt{2}+\sqrt{3}$, then $x+\frac{1}{x-1}$ will be equal to:

Find the value of $\sqrt{732108}$.

Find the value of:

$\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$

If the value of  $\sqrt{30}$ is approximately $5.477$, then what is the approximate value of  $\sqrt{\frac{5}{6}}$?

What should come in the place of $\left(?\right)$ for the expression given below?

$\frac{1}{\sqrt{8}-\sqrt{7}}-\frac{1}{\sqrt{7}-\sqrt{2}}+\frac{\sqrt{2}}{5}=?$

What should come in the place of $\left(?\right)$ for the expression given below?

$\sqrt{\frac{{\left(0.01\right)}^2}{{\left(0.001\right)}^2}+\frac{4{\left(\sqrt{1.414}\right)}^2}{2{\left(\sqrt{14.14}\right)}^2}}=?$

What should come in the place of $\left(?\right)$ for the expression given below?

$\frac{\sqrt{8}+\sqrt{4}+\sqrt{2}}{\sqrt{8}-\sqrt{4}-\sqrt{2}}+\frac{\sqrt{8}-\sqrt{4}+\sqrt{2}}{\sqrt{8}+\sqrt{4}-\sqrt{2}}=?$

What should come in the place of ($?$) for the expression given below?

$\left(\sqrt{15-2\sqrt{56}}\right)+\frac{1}{\left(\sqrt{15-2\sqrt{56}}\right)}=?$

Simplify & $x$

$\frac{{\left(729\right)}^{{\displaystyle \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}+{\left(27\right)}^{{\displaystyle \raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}{{\left(729\right)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}+{\left(27\right)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

Simplify

$\frac{pq\left(\sqrt{r^3\times p^3\times q^5}\right)}{\sqrt{pqr}{(r^2\times p^2\times q^2)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}}}=?$

Simplify

$\frac{8}{24+2\sqrt{5}}\times \frac{139}{4}$

Simplify

$\frac{12}{4+6\sqrt{3}}\times \frac{23}{6}$

Simplify the following expression:

$\frac{48}{2\sqrt{3}-4}$

Simplify the following expression using rule and properties of surds:

$\sqrt{\frac{4900\times 441}{4}}$

The value of $\sqrt{11+2\sqrt{18}}$ is closest to:

The expression $\sqrt{10+2\left(\sqrt{6}-\sqrt{15}-\sqrt{10}\right)}$ is equal to:

The value of $\sqrt{28+10\sqrt{3}}-\sqrt{7-4\sqrt{3}}$ is close to: