Question

rationalize the denominator root 6 - root 5 / root 6 + root 5
answer in full

Answer 1

Step-by-step explanation:

I hope it will help you and please mark me as brainliest.

Answer 2

Answer:

$\frac{\sqrt{6} -\sqrt{5} }{\sqrt{6} +\sqrt{5} }$ = 11 - 2$\sqrt{30}$

Step-by-step explanation:

Given expression is $\frac{\sqrt{6} -\sqrt{5} }{\sqrt{6} +\sqrt{5} }$

Rationalizing the denominator is the process of eliminating the irrational number from the denominator.

Rationalizing factor is $\sqrt{6} -\sqrt{5}$

Multiply the numerator and denominator with the rationalizing factor we get

$\frac{\sqrt{6} -\sqrt{5} }{\sqrt{6} +\sqrt{5} }$ ×$\frac{\sqrt{6} -\sqrt{5} }{\sqrt{6} -\sqrt{5} }$

= $\frac{(\sqrt{6} -\sqrt{5})^2 }{(\sqrt{6})^2 - (\sqrt{5})^2 }$

= $\frac{(\sqrt{6})^2 + (\sqrt{5})^2 - 2\sqrt{6} \sqrt{5} }{6 -5 }$

= $\frac{6 + 5 - 2\sqrt{30} }{1 }$

= 11 - 2$\sqrt{30}$

∴ The expression $\frac{\sqrt{6} -\sqrt{5} }{\sqrt{6} +\sqrt{5} }$ with rational denominator = 11 - 2$\sqrt{30}$

#SPJ2