(5sqrt3) / (sqrt3 - sqrt2)
i got 15 - 5sqrt2
but is that right???
Hi there.
The answer is $\displaystyle 15+5\sqrt{6}$ - obtained by multiplying the numerator and the denominator of the fraction by $\displaystyle \sqrt{3}+\sqrt{2}$ - the conjugate of $\displaystyle \sqrt{3}-\sqrt{2}$
$\displaystyle \frac{5 \sqrt{3}}{\sqrt{3}-\sqrt{2}}$
$\displaystyle \frac{5 \sqrt{3}(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}$
using the property
(a+b)(a-b) = a^2 - b^2 for denominator
we get
$\displaystyle \frac{5 \sqrt{3}(\sqrt{3}+\sqrt{2})}{3-2}$
$\displaystyle \frac{5*3+5\sqrt{2*3})}{1}$
$\displaystyle 15+5\sqrt{6}$
I think you messed up in last step