How do you simplify (√2+√5) /( √2-√5)?

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How do you simplify (√2+√5) /( √2-√5)?

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Answer 1 · 2018-03-16T22:59:50

The simplified expression is $- \frac{7 + 2 \sqrt{10}}{3}$ $-(7+2sqrt10)/3$ .

Explanation:

$= \frac{\sqrt{2} + \sqrt{5}}{\sqrt{2} - \sqrt{5}}$ $color(white)=(sqrt2+sqrt5)/(sqrt2-sqrt5)$

$= \frac{(\sqrt{2} + \sqrt{5})}{(\sqrt{2} - \sqrt{5})} \cdot \frac{(\sqrt{2} + \sqrt{5})}{(\sqrt{2} + \sqrt{5})}$ $=((sqrt2+sqrt5))/((sqrt2-sqrt5))color(red)(*((sqrt2+sqrt5))/((sqrt2+sqrt5)))$

$= \frac{(\sqrt{2} + \sqrt{5}) (\sqrt{2} + \sqrt{5})}{(\sqrt{2} - \sqrt{5}) (\sqrt{2} + \sqrt{5})}$ $=((sqrt2+sqrt5)(sqrt2+sqrt5))/((sqrt2-sqrt5)(sqrt2+sqrt5))$

$= \frac{(\sqrt{2} + \sqrt{5}) (\sqrt{2} + \sqrt{5})}{{\sqrt{2}}^{2} + \sqrt{2} \sqrt{5} - \sqrt{2} \sqrt{5} - {\sqrt{5}}^{2}}$ $=((sqrt2+sqrt5)(sqrt2+sqrt5))/(sqrt2^2+sqrt2sqrt5-sqrt2sqrt5-sqrt5^2)$

$=((sqrt2+sqrt5)(sqrt2+sqrt5))/(2color(red)cancelcolor(black)(+sqrt10-sqrt10)-5)$

$=((sqrt2+sqrt5)(sqrt2+sqrt5))/(2-5)$

$=((sqrt2+sqrt5)(sqrt2+sqrt5))/(-3)$

$=(sqrt2^2+sqrt2sqrt5+sqrt2sqrt5+sqrt5^2)/(-3)$

$=(2+sqrt10+sqrt10+5)/(-3)$

$=(2+2sqrt10+5)/(-3)$

$=(7+2sqrt10)/(-3)$

$=-(7+2sqrt10)/3$

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How do you simplify (√2+√5) /( √2-√5)?

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