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How do you simplify open parentheses 4 minus square root of 3 close parentheses open parentheses 12 plus 5 square root of 3 close parentheses?

1 Answer

Oct 9, 2015

$33 + 8 \sqrt{3}$ $33+8sqrt(3)$

Explanation:

Translation into workable form
4 minus square root of 3 close parentheses open parentheses 12 plus 5 square root of 3 close parentheses

$(4 - \sqrt{3}) (12 + 5 \sqrt{3})$ $(4-sqrt(3))(12+5sqrt(3))$

Evaluation
$(4 - \sqrt{3}) (12 + 5 \sqrt{3})$ $(color(red)(4-sqrt(3)))(color(blue)(12+5sqrt(3)))$

$XXX = 4 (12 + 5 \sqrt{3}) - \sqrt{3} (12 + 5 \sqrt{3})$ $color(white)("XXX")=color(red)(4)(color(blue)(12+5sqrt(3)))-color(red)(sqrt(3))(color(blue)(12+5sqrt(3)))$

$XXX = (48 + 20 \sqrt{3}) - (12 \sqrt{3} + 15)$ $color(white)("XXX")=(color(green)(48+20sqrt(3)))-(color(brown)(12sqrt(3)+15))$

$XXX = 33 + 8 \sqrt{3}$ $color(white)("XXX")=33+8sqrt(3)$

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