Question

Rationalize (4+√5)/(√15-√8)​

Answer 1

See attached picture

Explanation:

We rarionalize by multiplying with the conjugate of the denominator

Answer 2

`(4√(15) +8√(2)+5√(3) +2√(10) )/(7)`

Explanation:

`(4+√( 5))/(√(15)-√(8) )`

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

`(4+√( 5))/(√(15)-√(8) )*(√(15)+√(8) )/(√(15) +√(8) )`

We can simplify √8 like this :

√8 = √4 × √2

√8 = 2√2

Let us rationalize the above fraction now.

`(4+√( 5))/(√(15)-√(8) )*(√(15)+√(8) )/(√(15) +√(8) )\\ \\\\((4+√( 5)))/((√(15)-√(8)) )*((√(15)+2√(2) ) )/((√(15) +√(8)))`

Solve the brackets and roots.

`(4(√(15)+2√(2))+√(5) (√(15) +2√(2)) )/(√( 15) * √(15) - √(8) * √(8) ) }\\\\\\(4√(15) +8√(2)+√(75)+2√(10) )/(15-8)`

Simplify the roots.

√75 = √25 × √3

√75 = 5√3

`(4√(15) +8√(2)+√(75)+2√(10) )/(15-8)\\\\\\(4√(15) +8√(2)+5√(3) +2√(10) )/(7)`