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What is Square root of 2 - square root of 8 + 5 square root 18?

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Jun 2, 2015

$\sqrt{2} - \sqrt{8} + 5 \sqrt{18}$ $sqrt2 - sqrt8 +5sqrt18$

$\sqrt{8} = 2 \sqrt{2}$ $sqrt8 = color(blue)(2sqrt2$
$\sqrt{18} = 3 \sqrt{2}$ $sqrt18 = color(red)(3sqrt2$
$5 \sqrt{18} = 5 . 3 \sqrt{2} = 15 \sqrt{2}$ $5sqrt18 = 5 . color(red)(3sqrt2) = color(red)(15sqrt2$

rewriting the expression as:

$\sqrt{2} - 2 \sqrt{2} + 15 \sqrt{2}$ $sqrt2 - color(blue)(2sqrt2+ color(red)(15sqrt2$

$(15 \sqrt{2} - 2 \sqrt{2} = 13 \sqrt{2})$ $(15sqrt2 - 2sqrt2 = 13sqrt2)$

$= \sqrt{2} + 13 \sqrt{2}$ $=sqrt2 + 13sqrt2$
$= 14 \sqrt{2}$ $=color(green)(14sqrt2$
$\approx 19.796$ $approx color(green)(19.796$

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