How do you simplify (1/sqrt3) + (1/sqrt 2)?

Jun 14, 2017

see below

Explanation:

$\frac{\sqrt{3}}{3} + \frac{\sqrt{2}}{2} = \frac{3 \sqrt{2} + 2 \sqrt{3}}{6}$

Jun 19, 2017

$= \frac{2 \sqrt{3} + 3 \sqrt{2}}{6}$

Explanation:

Add in the same way as with any fractions: find the LCD

1/sqrt3 + 1/sqrt2 = (??????)/(sqrt3 xx sqrt2)

Find equivalent fractions:

$\frac{\sqrt{2} + \sqrt{3}}{\sqrt{3} \times \sqrt{2}} = \frac{\sqrt{2} + \sqrt{3}}{\sqrt{6}}$

Rationalise the denominator by multiplying by $\frac{\sqrt{6}}{\sqrt{6}}$

$\frac{\sqrt{2} + \sqrt{3}}{\sqrt{6}} \times \frac{\sqrt{\textcolor{b l u e}{6}}}{\sqrt{6}} = \frac{\textcolor{b l u e}{\sqrt{2} \times \sqrt{3}} \left(\sqrt{2} + \sqrt{3}\right)}{{\sqrt{6}}^{2}}$

$= \frac{2 \sqrt{3} + 3 \sqrt{2}}{6}$