Rationalize frac 2 sqrt 3 3 sqrt 2 3 sqrt 2 - 2... - JAMB Mathematics 1991 Question
Rationalize (\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}})
A
5 - 2\(\sqrt{6}\)
B
5 + 2\(\sqrt{6}\)
C
5\(\sqrt{6}\)
D
5
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Correct Option: B
(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}})
= (\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}) x (\frac{3\sqrt{2} + 2 \sqrt{3}}{3\sqrt{2} - 2 \sqrt{3}})
(\frac{4(3) + 9(2) + 2(6) \sqrt{6}}{9(2) - 4(3)})
(\frac{12 + 18 + 12\sqrt{6}}{1`8 - 12})
= (\frac{30 + 12\sqrt{6}}{6})
= 5 + 2(\sqrt{6})
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