Simplify frac 5 sqrt 3 - frac 3 sqrt 2 - WAEC Mathematics 2005 Question
Simplify \(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}\)
A
\(\frac{1}{6}(5\sqrt{3}-3\sqrt{2}\)
B
\(\frac{1}{6}(15\sqrt{3}-6\sqrt{2}\)
C
\(\frac{1}{6}(3\sqrt{2}-\sqrt{3}\)
D
\(\frac{1}{6}(10\sqrt{3}-9\sqrt{2}\)
correct option: d
\(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}}\
=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}}Rationalize\
\frac{\sqrt{6}(5\sqrt{2}-3\sqrt{3})}{6}\
\frac{5\sqrt{12}-3\sqrt{18}}{6}=\frac{10\sqrt{3}-9\sqrt{2}}{6}\
\frac{1}{6}(10\sqrt{3}-9\sqrt{2})\)
=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}}Rationalize\
\frac{\sqrt{6}(5\sqrt{2}-3\sqrt{3})}{6}\
\frac{5\sqrt{12}-3\sqrt{18}}{6}=\frac{10\sqrt{3}-9\sqrt{2}}{6}\
\frac{1}{6}(10\sqrt{3}-9\sqrt{2})\)
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