How do you simplify $\frac{2 \sqrt{3} + \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}$ $(2sqrt3+sqrt2)/(sqrt3+2sqrt2)$ ?

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How do you simplify $\frac{2 \sqrt{3} + \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}$ $(2sqrt3+sqrt2)/(sqrt3+2sqrt2)$ ?

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Answer 1 · 2015-04-03T12:20:50

Multiply both numerator (top) and denominator (bottom) by the conjugate (see example) of the denominator.

$\frac{2 \sqrt{3} + \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}} \cdot \frac{\sqrt{3} - 2 \sqrt{2}}{\sqrt{3} - 2 \sqrt{2}}$ $(2sqrt(3)+sqrt(2))/(sqrt(3)+2sqrt(2))*(sqrt(3)-2sqrt(2))/(sqrt(3)-2sqrt(2))$

$= \frac{2 (3) + \sqrt{2} \sqrt{3} - 4 \sqrt{2} \sqrt{3} - 2 (2)}{3 - 8}$ $= (2(3) +sqrt(2)sqrt(3)-4sqrt(2)sqrt(3)-2(2))/(3-8)$

$= \frac{10 - 3 \sqrt{6}}{- 5}$ $=(10 - 3sqrt(6))/(-5)$

$= \frac{3}{5} \sqrt{6} - 2$ $= 3/5sqrt(6) -2$

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How do you simplify $\frac{2 \sqrt{3} + \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}$ $(2sqrt3+sqrt2)/(sqrt3+2sqrt2)$ ?

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