Question

rationalization 1/5+3√2​

Answer 1

Answer:

$\frac{1}{5 + 3 \sqrt{2} } = \frac{5 - 3 \sqrt{2} }{7}$

Step-by-step explanation:

$\frac{1}{5 + 3 \sqrt{2} } \\ = \frac{1}{5 + 3 \sqrt{2} } \times \frac{5 - 3 \sqrt{2} }{5 - 3 \sqrt{2} } \\ = \frac{1(5 - 3 \sqrt{2} )}{(5 + 3 \sqrt{2} )(5 - 3 \sqrt{2}) } \\ = \frac{5 - 3 \sqrt{2} }{ {(5)}^{2} - {(3 \sqrt{2}) }^{2} } \\ = \frac{5 - 3 \sqrt{2} }{25 - 18} \\ = \frac{5 - 3 \sqrt{2} }{7}$