(5sqrt3) / (sqrt3 - sqrt2)

i got 15 - 5sqrt2

but is that right???

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- Dec 2nd 2009, 10:30 PMdeej813rationalise
(5sqrt3) / (sqrt3 - sqrt2)

i got 15 - 5sqrt2

but is that right??? - Dec 2nd 2009, 11:23 PMStroodle
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 $\displaystyle \sqrt{3}-\sqrt{2}$ - Dec 2nd 2009, 11:36 PMADARSH
$\displaystyle \frac{5 \sqrt{3}}{\sqrt{3}-\sqrt{2}}$

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

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