Question

Rationalize (4+√5)/(√15-√8)​

Answer 1

Answer:

$\frac{4\sqrt{15} +8\sqrt{2}+5\sqrt{3} +2\sqrt{10} }{7}$

Step-by-step explanation:

$\frac{4+\sqrt{ 5}}{\sqrt{15}-\sqrt{8} }$

To rationalize the above fraction multiple both numerator and denominator by the conjugate of its denominator.

$\frac{4+\sqrt{ 5}}{\sqrt{15}-\sqrt{8} }*\frac{\sqrt{15}+\sqrt{8} }{\sqrt{15} +\sqrt{8} }$

We can simplify √8 like this :

√8 = √4 × √2

√8 = 2√2

Let us rationalize the above fraction now.

$\frac{4+\sqrt{ 5}}{\sqrt{15}-\sqrt{8} }*\frac{\sqrt{15}+\sqrt{8} }{\sqrt{15} +\sqrt{8} }\\ \\\\\frac{(4+\sqrt{ 5})}{(\sqrt{15}-\sqrt{8}) }*\frac{(\sqrt{15}+2\sqrt{2} ) }{(\sqrt{15} +\sqrt{8})}$

Solve the brackets and roots.

$\frac{4(\sqrt{15}+2\sqrt{2})+\sqrt{5} (\sqrt{15} +2\sqrt{2}) }{\sqrt{ 15} * \sqrt{15} - \sqrt{8} * \sqrt{8} } }\\\\\\\frac{4\sqrt{15} +8\sqrt{2}+\sqrt{75}+2\sqrt{10} }{15-8}$

Simplify the roots.

√75 = √25 × √3

√75 = 5√3

$\frac{4\sqrt{15} +8\sqrt{2}+\sqrt{75}+2\sqrt{10} }{15-8}\\\\\\\frac{4\sqrt{15} +8\sqrt{2}+5\sqrt{3} +2\sqrt{10} }{7}$

Answer 2

Answer:

See attached picture

Step-by-step explanation:

We rarionalize by multiplying with the conjugate of the denominator