Question

Need help with Simplifying expressions.

Answer 1

Multiply be the complex congugate


`(9)/(3 - √(2) ) * (3+ √(2) )/(3+ √(2) ) = (27+9 √(2) )/(9- √(2)+ √(2) - 2) = (27+9 √(2) )/(7)`

Next one, prime factor the roots

`2 √(54) - 5 √(24) \\ \\ 2 √(2*3*3*3) - 5 √(2*3*2*2) = 2 *3 √(2*3) - 5*2 √(2*3) \\ \\ = 6 √(6)-10 √(6) = -4 √(6)`

Rationalize the denominator

`(5)/( √(11) ) * ( √(11) )/( √(11) ) = (5 √(11) )/(11)`