Question

rationalize the denominator root 5 minus root 3 upon root 5 + root 3​

Answer 1

Answer:

Rationalize the denominator of:-

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

Solution:-

$= \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$

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

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

$= \frac{5 + 3 - 2 \sqrt{15} }{2}$

$= \frac{ 8 - 2 \sqrt{15} }{2}$

$= 4 - 2 \sqrt{15}$

Step-by-step explanation:

Hope this helps you.

# By Sparkly Princess