Question

Rationalize the denominator ​

Answer 1

The answer is

`(84 - 31 √(6) )/(30)`

Explanation:

`(5 √(3) - 4 √(2) )/(4 √(3) + 3√(2) )`

To rationalize the denominator multiply both the numerator and the denominator by

4√3 - 3√2

That's

`(5 √(3) - 4√(2) )/(4 √(3) + 3 √(2) ) * (4 √(3) - 3 √(2) )/(4 √(3) - 3 √(2) )`

So we have

`((5 √(3) - 4 √(2))(4 √(3) - 3 √(2)) )/((4 √(3) + 3 √(2) )(4 √(3) - 3 √(2) ) ) \\ = (60 - 15 √(6) - 16 √(6) + 24 )/(16(3) - 9(2)) \\ = (84 - 15 √(6) - 16 √(6) )/(48 - 18) \\ = (84 - 31 √(6) )/(48 - 18)`

We have the final answer as

`(84 - 31 √(6) )/(30)`

Hope this helps you