Question

Rationalize the denominator and write irrational number to its simplest form. 6−4√3 / 6+4√3

Answer 1

Answer:

$= \frac{6 - 4 \sqrt{3} }{6 + 4 \sqrt{3} } \\ = \frac{6 - 4 \sqrt{3} }{6 + 4 \sqrt{3} } \times \ \frac{6 - 4 \sqrt{3} }{6 - 4 \sqrt{3} } \\ = \frac{(6 - 4 \sqrt{3) {}^{2} } }{(6) {}^{2} - (4 \sqrt{3}) {}^{2} } \\ = (6) {}^{2} - 2 \times 6 \times 4 \sqrt{3} + 4 \sqrt{3 } {}^{2} \div 36 - 48 \\ = 36 - 48 \sqrt{3} + 48 \div - 12 \\ = \frac{36 \sqrt{3} }{ - 12} \\ = - 3 \sqrt{3}$

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