Question

rationalize underroot 3-5 underroot 2 upon underroot 3+5 underroot 2​

Answer 1

Answer:

$\frac{10 \sqrt{6} - 53}{47}$

Step-by-step explanation:

$\frac{ \sqrt{3} - 5 \sqrt{2} }{ \sqrt{ 3} + 5\sqrt{2} }$

Rationalizing we get

$\frac{ {( \sqrt{3} - 5 \sqrt{2} )}^{2} }{ { \sqrt{ 3} }^{2} - {(5 \sqrt{2)} }^{2} }$

$= \frac{3 + 50 - 10 \sqrt{6} }{ - 47}$

$\frac{10 \sqrt{6} - 53 }{47}$