Surds & Indices

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

For any natural number $$ n $$, let $$ a_n $$ be the largest integer not exceeding $$ \sqrt{n} $$. Then, the value of $$...

The sum of all real values of $$ k $$ for which $$ \left(\frac{1}{8}\right)^k\times\left(\frac{1}{32768}\right)^{\frac...

Let $$a, b, m,$$ and $$n$$ be natural numbers such that $$a > 1$$ and $$b > 1$$. If $$a^m b^n = 144^{145}$$, then the l...

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