How do you multiply ${(\sqrt{3} + 2 \sqrt{5})}^{2}$ $(sqrt3+ 2sqrt5)^2$ ?

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How do you multiply ${(\sqrt{3} + 2 \sqrt{5})}^{2}$ $(sqrt3+ 2sqrt5)^2$ ?

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Answer 1 · 2015-07-05T13:15:21

${(\sqrt{3} + 2 \sqrt{5})}^{2}$ $(sqrt(3)+2sqrt(5))^2$
$XXXX$ $color(white)("XXXX")$

Explanation:

${(\sqrt{3} + 2 \sqrt{5})}^{2}$ $(sqrt(3)+2sqrt(5))^2$
$XXXX$ $color(white)("XXXX")$ $= (\sqrt{3} + 2 \sqrt{5}) \cdot (\sqrt{3} + 2 \sqrt{5})$ $=color(red)((sqrt(3)+2sqrt(5)))*color(blue)((sqrt(3)+2sqrt(5)))$

$XXXX$ $color(white)("XXXX")$ $= (\sqrt{3} + 2 \sqrt{5}) \cdot (\sqrt{3}) + (\sqrt{3} + 2 \sqrt{5}) \cdot (2 \sqrt{5})$ $=color(red)((sqrt(3)+2sqrt(5)))*color(blue)((sqrt(3)))+color(red)((sqrt(3)+2sqrt(5)))*color(blue)((2sqrt(5))$

$XXXX$ $color(white)("XXXX")$ $= (\sqrt{3}) \cdot (\sqrt{3}) + (2 \sqrt{5}) \cdot (\sqrt{3}) + (\sqrt{3}) \cdot (2 \sqrt{5}) + (2 \sqrt{5}) \cdot (2 \sqrt{5})$ $= color(red)((sqrt(3)))*color(blue)((sqrt(3))) +color(red)((2sqrt(5))*color(blue)((sqrt(3)))+color(red)((sqrt(3))*color(blue)((2sqrt(5)))+color(red)((2sqrt(5)))*color(blue)((2sqrt(5)))$

$XXXX$ $color(white)("XXXX")$ $= 3 + 2 \sqrt{15} + 2 \sqrt{15} + 20$ $= 3 + 2sqrt(15) + 2sqrt(15) + 20$

$XXXX$ $color(white)("XXXX")$ $= 23 + 4 \sqrt{15}$ $=23 + 4sqrt(15)$

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How do you multiply ${(\sqrt{3} + 2 \sqrt{5})}^{2}$ $(sqrt3+ 2sqrt5)^2$ ?

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