Answer
$30x^{3/2}$ and $30\sqrt3x$
Work Step by Step
The $r+1$ th term in the binomial expansion of $(x+y)^n$ is:
$\binom{n}{r}x^{n-r}y^r$
Here $x=\sqrt{x}$, $y=\sqrt{3}$, $n=5$:
There are 6 terms in this expansion, the middle two are the 3 rd and 4th.
3rd term:
$r+1=3$
$r=2$
$\binom{5}{2}(\sqrt{x})^{5-2}(\sqrt{3})^2=10x^{3/2}\times 3=30x^{3/2}$
4th term:
$r+1=4$
$r=3$
$\binom{5}{3}(\sqrt{x})^{5-3}(\sqrt{3})^3=10x\times 3\sqrt3=30\sqrt3x$
