Question #1eeb2

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Question #1eeb2

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Answer 1 · 2017-03-01T20:37:00

$2 \sqrt{3}$ $2sqrt(3)$

Explanation:

In this format the brackets do not do anything so disregard them.

$\frac{15}{\sqrt{3}} - \sqrt{27}$ $15/sqrt(3)-sqrt(27)$

Mathematicians do not like roots in the denominator so lets 'get rid' of it. Multiply by 1 and you do not change a value. However, 1 comes in many forms so you can change the way something looks without changing its intrinsic value.

$[\frac{15}{\sqrt{3}} \times 1] - \sqrt{27}$ $color(green)([15/sqrt(3)color(red)(xx1)]-sqrt(27)$

$[\frac{15}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}] - \sqrt{27}$ $color(green)([15/sqrt(3)color(red)(xxsqrt(3)/sqrt(3))]-sqrt(27)$

$[\frac{15 \sqrt{3}}{3}] - \sqrt{27}$ $color(green)([(15sqrt(3))/3]-sqrt(27))$

But $\sqrt{27} = \sqrt{3 \times 9} = \sqrt{3 \times 3^{2}} = 3 \sqrt{3}$ $sqrt(27) = sqrt(3xx9)=sqrt(3xx3^2)=3sqrt(3)$

$\frac{15 \sqrt{3}}{3} - 3 \sqrt{3}$ $(15sqrt(3))/3-3sqrt(3)$

Factor out the $\sqrt{3}$ $sqrt(3)$

$\sqrt{3} \times [\frac{15}{3} - 3]$ $sqrt(3)xx[15/3-3]$

$\sqrt{3} \times \frac{6}{3}$ $sqrt(3)xx6/3$

$2 \sqrt{3}$ $2sqrt(3)$

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Question #1eeb2

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