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Q8 (continued from previous response):

May 21, 2026Psychology

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Answer

5 + \frac{10}{3}\sqrt{3}

2 steps

Q8 (continued from previous response):

= \frac{2(3-\sqrt{3})}{3^2 - (\sqrt{3})^2} = \frac{6-2\sqrt{3}}{9-3} = \frac{6-2\sqrt{3}}{6}

Simplify the second term:

= \frac{6}{6} - \frac{2\sqrt{3}}{6} = 1 - \frac{\sqrt{3}}{3}

Subtract the simplified second term from the simplified first term.
The first term was found in Step 1 to be $6+3\sqrt{3}$ .
$(6+3\sqrt{3}) - \left(1 - \frac{\sqrt{3}}{3}\right)$ $= 6+3\sqrt{3} - 1 + \frac{\sqrt{3}}{3}$
Combine the rational and irrational parts.
$= (6-1) + \left(3\sqrt{3} + \frac{\sqrt{3}}{3}\right)$ $= 5 + \left(\frac{9\sqrt{3}}{3} + \frac{\sqrt{3}}{3}\right)$ $= 5 + \frac{10\sqrt{3}}{3}$
The expression in the form $m+n\sqrt{3}$ is $\boxed{5 + \frac{10}{3}\sqrt{3}}$ .

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