# rationalise

• December 2nd 2009, 10:30 PM
deej813
rationalise
(5sqrt3) / (sqrt3 - sqrt2)

i got 15 - 5sqrt2

but is that right???
• December 2nd 2009, 11:23 PM
Stroodle
Hi there.

The answer is $15+5\sqrt{6}$ - obtained by multiplying the numerator and the denominator of the fraction by $\sqrt{3}+\sqrt{2}$ - the conjugate of $\sqrt{3}-\sqrt{2}$
• December 2nd 2009, 11:36 PM
Quote:

Originally Posted by deej813
(5sqrt3) / (sqrt3 - sqrt2)

i got 15 - 5sqrt2

but is that right???

$\frac{5 \sqrt{3}}{\sqrt{3}-\sqrt{2}}$

$\frac{5 \sqrt{3}(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}$
using the property
(a+b)(a-b) = a^2 - b^2 for denominator
we get

$\frac{5 \sqrt{3}(\sqrt{3}+\sqrt{2})}{3-2}$

$\frac{5*3+5\sqrt{2*3})}{1}$

$15+5\sqrt{6}$
I think you messed up in last step