How do you simplify (3 sqrt(2) + 2 sqrt(5))(4 sqrt(2) - sqrt(5))?

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How do you simplify (3 sqrt(2) + 2 sqrt(5))(4 sqrt(2) - sqrt(5))?

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Answer 1 · 2018-06-20T17:03:47

$\frac{34 + 11 \sqrt{10}}{27}$ $frac{34 + 11 sqrt 10}{27}$

Explanation:

$\frac{3 \sqrt{2} + 2 \sqrt{5}}{4 \sqrt{2} - \sqrt{5}} \cdot \frac{4 \sqrt{2} + \sqrt{5}}{4 \sqrt{2} + \sqrt{5}}$ $frac{3 sqrt 2 + 2 sqrt 5}{4 sqrt 2 - sqrt 5} * frac{4 sqrt 2 + sqrt 5}{4 sqrt 2 + sqrt 5}$

$= \frac{24 + 3 \sqrt{10} + 8 \sqrt{10} + 10}{32 - 5}$ $= frac{24 + 3 sqrt 10 + 8 sqrt 10 + 10}{32 - 5}$

$= \frac{34 + 11 \sqrt{10}}{27}$ $= frac{34 + 11 sqrt 10}{27}$

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How do you simplify (3 sqrt(2) + 2 sqrt(5))(4 sqrt(2) - sqrt(5))?

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