The product of two conjugate binomial surds is ...........

Show that the cube of any positive integer is of the form $4m, 4m+1$ or $4m+3$ for some integer $m$.

Express $404$ as a product of primes.

On a morning walk,three persons step off together and their steps measure $40\, cm$,$42\, cm$ and $45\, cm$,respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps? (in $cm$)

If two positive integers $p$ and $q$ can be expressed as $p = a b^{2}$ and $q = a^{3} b$,where $a$ and $b$ are prime numbers,then $LCM(p, q)$ is:

Prove that the following number is irrational: $\frac{1}{\sqrt{3}}$