Question

What would be the denominator after rationalizing 5/(5√2+ 5√3)?​

Answer 1

$= \frac{5}{5 \sqrt{2} + 5 \sqrt{3} } \times \frac{5 \sqrt{2} - 5 \sqrt{3} }{5 \sqrt{2} - 5 \sqrt{3} } \\ \\ = \frac{5(5 \sqrt{2} - 5 \sqrt{3} )}{(5 \sqrt{2}) {}^{2} - (5 \sqrt{3} ) {}^{2} } \\ \\ = \frac{25 \sqrt{2} - 25 \sqrt{3} }{50 - 75 } \\ \\ = \frac{25 \sqrt{2} - 25 \sqrt{3} }{ - 25} \\ \\ = 25( \frac{ \sqrt{2} - \sqrt{3} }{ - 1} ) \\ \\ = \frac{ \sqrt{2} - \sqrt{3} }{ - 1}$