How do you simplify $\sqrt{27} - \sqrt{8} + 2 \sqrt{2}$ $sqrt(27) - sqrt(8) + 2 sqrt(2)$ ?

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How do you simplify $\sqrt{27} - \sqrt{8} + 2 \sqrt{2}$ $sqrt(27) - sqrt(8) + 2 sqrt(2)$ ?

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Answer 1 · 2016-02-28T01:35:13

It is

$\sqrt{27} - \sqrt{8} + 2 \sqrt{2} = 3 \cdot \sqrt{3} - 2 \sqrt{2} + 2 \sqrt{2} = 3 \cdot \sqrt{3}$ $sqrt(27) - sqrt(8) + 2 sqrt(2)=3*sqrt3-2sqrt2+2sqrt2=3*sqrt3$

Answer 2 · 2016-02-28T01:38:52

$3 \sqrt{3}$ $3sqrt(3)$

Explanation:

Since
$XXX \sqrt{27} = \sqrt{3^{2} \cdot 3} = 3 \sqrt{3}$ $color(white)("XXX")color(red)(sqrt(27) = sqrt(3^2*3) = 3sqrt(3))$
and
$XXX \sqrt{8} = \sqrt{2^{2} \cdot 2} = 2 \sqrt{2}$ $color(white)("XXX")color(blue)(sqrt(8) = sqrt(2^2*2) = 2sqrt(2))$

Therefore
$XXX \sqrt{27} - \sqrt{8} + 2 \sqrt{2}$ $color(white)("XXX")color(red)(sqrt(27)-color(blue)(sqrt(8) + color(green)(2sqrt(2)$

$color(white)("XXX")= color(red)(3sqrt(3))cancel(-color(blue)(2sqrt(2)))cancel(+color(green)(2sqrt(2)))$

$color(white)("XXX")=3sqrt(3)$

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How do you simplify $\sqrt{27} - \sqrt{8} + 2 \sqrt{2}$ $sqrt(27) - sqrt(8) + 2 sqrt(2)$ ?

2 Answers

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