Question

5√2 + 4√3 ➗ 5√2 - 4√3 rationalize the denominator and simplify​

Answer 1

$= \frac{5 \sqrt{2} + 4 \sqrt{3} }{5 \sqrt{2} - 4 \sqrt{3} } \\ \\ = \frac{5 \sqrt{2} + 4 \sqrt{3} }{5 \sqrt{2} - 4 \sqrt{3} } \times \frac{5 \sqrt{2} + 4 \sqrt{3} }{5 \sqrt{2} + 4 \sqrt{3} } \\ \\ = \frac{ {(5 \sqrt{2} + 4 \sqrt{3} )}^{2} }{ {(5 \sqrt{2} )}^{2} - {(4 \sqrt{3} )}^{2} } \\ \\ = \frac{ ({5 \sqrt{2})}^{2} + {(4 \sqrt{3} )}^{2} + 2 \times 5 \sqrt{2} \times 4 \sqrt{3} }{50 - 48} \\ \\ = \frac{50 + 48 + 40 \sqrt{6} }{2} \\ \\ = \frac{2(25 + 24 + 20 \sqrt{6} )}{2} \\ \\ = 49 + 20 \sqrt{6}$