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:

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

Find the value of:

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

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

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

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:

If$\frac{(4\surd 3+5\surd 2)}{(\surd 48 + \surd 18)}=x+y\surd 6$ then find the values of x and y.

Four positions of a dice are given below, Identify the number at the bottom then the top is 6.

The value of  ${\left(1^3+2^3+3^3+4^3\right)}^{\frac{-3}{2}}$ will be

The value of $(-1{)}^{1000}$  is?

$\left(3p^{2}q{r}^3\right)\times \left(-4p^{3}q{r}^2\right)\times \left(7p{q}^{3}r\right)$ is equal to:

Evaluate the given expression:

${\left(\frac{3}{4}\right)}^7\times {\left(\frac{4}{3}\right)}^7=?$

$\sqrt[3]{\sqrt[2]{0.000064}}$ is equal to:

If     $2\sqrt{\mathrm{x}}=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$   ,then the value of x is:

Which of the following is greatest ?