Question

Rationalize the denominator- root 11 - root 5 / root 11 + root 5


Please answer ASAP.

Answer 1

Answer:

(root 11 - root 5)² / 6

Step-by-step explanation:

Multiply numerator and denominator by (root 11 - root 5)

Use the formula

(a-b)*(a+b) = a²-b²

Answer 2

$\frac{ \sqrt{11} - \sqrt{5} }{ \sqrt{11} + \sqrt{5} }$

$= > \frac{ \sqrt{11} - \sqrt{5} }{ \sqrt{11} + \sqrt{5} } \times \frac{ \sqrt{11} - \sqrt{5} }{ \sqrt{11} - \sqrt{5} }$

Using 1st and 3rd Identity in this equation

$=>\frac{ { (\sqrt{11} )}^{2} + { (\sqrt{5}) }^{2} + 2 \sqrt{11} \times \sqrt{5} }{ {( \sqrt{11} )}^{2} - { (\sqrt{5} )}^{2} }$

$=> \frac{11 + 5 + 2 \sqrt{55} }{11 - 5}$

$=> \frac{16 + 2 \sqrt{55} }{6}$