For any natural number n n n , let a n a_n a n ​ be the largest integer not exceeding n \sqrt{n} n ​ . Then, the value of a 1 + a 2 + ⋯ + a 50 a_1 + a...

If $$ (a + b\sqrt{n}) $$ is the positive square root of $$ (29 - 12\sqrt{5}) $$, where $$ a $$ and $...

The sum of all real values of $$ k $$ for which $$ \left(\frac{1}{8}\right)^k\times\left(\frac{1}{...

Which of the following is the greatest?...

If $$x = 5 + 2\sqrt{6}$$, find the value of $$\frac{x - 1}{\sqrt{x}}$$. ...

### Question Statement: Find the value of the expression: $$ \sqrt{4 + \sqrt{15}} + \sqrt{4 - \sqr...

If $$m$$ and $$n$$ are natural numbers such that $$n > 1$$, and $$m^n = 2^{25} \times 3^{40}$$, then...