3√(5) √(7)3√(3) √(2) =3√(5) √(7)3√(3) √(2)×3√(3)+√(2)3√(3)+√(2) =9√(15)+3√(10) 3√(21) √(14)27 2 =9√(15)+3√(10) 3√(21) √(14)25 ...

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Addition and Subtraction of Like and Unlike Surds

Solve: 3√5-...

Question

Solve: $\frac{3 \sqrt{5} - \sqrt{7}}{3 \sqrt{3} + \sqrt{2}}$

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Solution

$\frac{3 \sqrt{5} - \sqrt{7}}{3 \sqrt{3} - \sqrt{2}}$
$= \frac{3 \sqrt{5} - \sqrt{7}}{3 \sqrt{3} - \sqrt{2}} \times \frac{3 \sqrt{3} + \sqrt{2}}{3 \sqrt{3} + \sqrt{2}}$
$= \frac{9 \sqrt{15} + 3 \sqrt{10} - 3 \sqrt{21} - \sqrt{14}}{27 - 2}$
$= \frac{9 \sqrt{15} + 3 \sqrt{10} - 3 \sqrt{21} - \sqrt{14}}{25}$

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