Surds and Indices Level - 1

Evaluate: $\sqrt{248 + \sqrt{52 + \sqrt{144}}}$

What will come in place of the question mark?

 $\sqrt{86.49} + \sqrt{5 + (?)^2} = 12.3$

Find the value of $\sqrt{\frac{0.289}{0.00121}}$

Simplify: $\frac{1}{\sqrt{100}-\sqrt{99}} - \frac{1}{\sqrt{99}-\sqrt{98}} + \frac{1}{\sqrt{98}-\sqrt{97}} - \dots + \frac{1}{\sqrt{2}-\sqrt{1}}$

Find the sum: $3 + \frac{1}{\sqrt{3}} + \frac{1}{3+\sqrt{3}} - \frac{1}{3-\sqrt{3}}$

If $x = \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$ and $y = \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$, find $(x^2+y^2)$

Find the value of $\sqrt{6+\sqrt{6+\sqrt{6+\dots}}}$

By what least number must $4320$ be multiplied to obtain a perfect cube?

$\sqrt{53824} = ?$

The square root of 41209 is equal to