How do you simplify $(sqrt(3) - 2) / (-5*sqrt(3)+8)$ ?

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How do you simplify $(sqrt(3) - 2) / (-5*sqrt(3)+8)$ ?

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Answer 1 · 2017-06-12T17:41:40

$color(green)((1+2sqrt3)/11$

Explanation:

$(sqrt3-2)/(-5*sqrt3+8)$

$(sqrt3-2)/(-5*sqrt3+8) xx (-5sqrt3-8)/(-5sqrt3-8)$ (conjugate)

$color(white)(aaaaaaaaaaaaa)$ $sqrt3-2$
$color(white)(aaaaaaaa)$ $xx underline(-5sqrt3-8)$
$color(white)(aaaaaaaaaaaaa)$ $(-5*3)+10sqrt3$
$color(white)(aaaaaaaaaaaaaaaaaaaaaa)$ $-8sqrt3+16$
$color(white)(aaaaaaaaaaaaaaaaaa)$ $overline(-15+2sqrt3+16)$

$color(white)(aaaaaaaaaaaaa)$ $color(green)(1+2sqrt3$ numerator

$color(white)(aaaaaaaaaaaaa)$ $-5sqrt3+8$
$color(white)(aaaaaaaaaaa)$ $xx underline(-5sqrt3-8)$
$color(white)(aaaaaaaaaaaaa)$ $(25*3)-40sqrt3$
$color(white)(aaaaaaaaaaaaaaaaaaaa)$ $ul(+40sqrt3-64)$
$color(white)(aaaaaaaaaaaaaaaaaa)$ $75-64$

$color(white)(aaaaaaaaaaaaa)$ $color(green)(11$ denominator

$:.color(green)(=(1+2sqrt3)/11$

Check:

$color(red)((sqrt3-2)/(-5*sqrt3+8)=0.405827418$

$color(red)((1+2sqrt3)/11=0.405827418$

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How do you simplify $(sqrt(3) - 2) / (-5*sqrt(3)+8)$ ?

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Explanation:

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How do you simplify $(sqrt(3) - 2) / (-5*sqrt(3)+8)$ ?