Get the answer to "To calculate: The simplification of the expression 33+653−26"

Ernstfalld

Answered question

2021-08-11

To calculate: The simplification of the expression

\frac{3 \sqrt{3} + \sqrt{6}}{5 \sqrt{3} - 2 \sqrt{6}}

Answer & Explanation

Cullen

Skilled2021-08-12Added 89 answers

The answer is given below

2021-12-24

Step1

$\frac{3 \sqrt{3} + \sqrt{6}}{5 \sqrt{3} - 2 \sqrt{6}} = \frac{3 \sqrt{3} + \sqrt{6}}{5 \sqrt{3} - 2 \sqrt{6}} \times \frac{5 \sqrt{3} + 2 \sqrt{6}}{5 \sqrt{3} + 2 \sqrt{6}}$
$= \frac{(3 \sqrt{3} + \sqrt{6}) (5 \sqrt{3} + 2 \sqrt{6})}{(5 \sqrt{3})^{2} - (2 \sqrt{6})^{2}}$
$= \frac{3 \sqrt{3} (5 \sqrt{3}) + 3 \sqrt{3} (2 \sqrt{6}) + \sqrt{6} (5 \sqrt{3}) + \sqrt{6} (2 \sqrt{6})}{75 - 24}$
$= \frac{45 + 6 \sqrt{18} + 5 \sqrt{18} + 12}{51}$
Further, simplify
$\frac{3 \sqrt{3} + \sqrt{6}}{5 \sqrt{3} - 2 \sqrt{6}} = \frac{57 + 11 \sqrt{18}}{51}$
$= \frac{57 + 11 \sqrt{3^{2} \times 2}}{51}$
$= \frac{57 + 33 \sqrt{2}}{51}$
$= \frac{3 (19 + 11 \sqrt{2})}{51}$
Hence, the simplification of the given expression is $\frac{19 + 11 \sqrt{2}}{17}$

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