Surds

If $\frac{x}{\sqrt{512}}=\frac{\sqrt{648}}{x}$, then find the value of $x?$

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

$\frac{2+\sqrt{3}}{2-\sqrt{3}}=?$, If $\sqrt{3}=1.732$

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

$\sqrt[3]{{\left(256\right)}^{-\frac{1}{8}}{\times \left(81\right)}^{\frac{3}{4}}\times {\left(64\right)}^{\frac{2}{3}}} =?$

The square root of $\sqrt [ 3 ]{ 4 } +\sqrt [ 3 ]{ 16 } +1$ is:

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

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

$\sqrt{8}+2\sqrt{32}-3\sqrt{128}+4\sqrt{50}=?$

Take $\sqrt{2} =1.414$

The value of $\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4......}}}}}}$ is _________.

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

What is the value of $\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+..................+\frac{1}{\sqrt{24}+\sqrt{25}}$?

What is the value of $\sqrt{4+\sqrt{15}}$?

The greatest of $\sqrt{2},\sqrt[6]{3},\sqrt[3]{4},\sqrt[4]{5}$ is.

If $x=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $y=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$, then the value of $\left(x^3+y^3\right)$ is:

The irrational number $\frac{8}{3+\sqrt{n}}$ when rationalized becomes $3-\sqrt{n}$. What is the value of $n$?

$9\sqrt{x}=\sqrt{12}+\sqrt{147}$ then find $x=?$

$\frac{\sqrt{10\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}}{\sqrt[3]{8}}=?$

Find the value of x and y? If $\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=x+7\sqrt{5}y$

$\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}$ is equal to?

The simplest value of $\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}=?$

$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+7\sqrt{5}b$

Find the value of $a$ and $b$.

Find the value of

$\sqrt[3]{-121+\sqrt[3]{-61+\sqrt[3]{-26+\sqrt[3]{-1}}}}$