Rationalize the denominator

Question

√10/√5-2

Answer 1

To rationalize √10/(√5 - 2), multiply the numerator and denominator by the conjugate of the denominator, 

√5 + 2.  numerator:√10(√5 + 2) = √50 + 2√10

                                                  = 5√2 + 2√10

 

             denominator:  (√5 - 2)(√5 + 2) = 5 - 4 = 1

 

ANSWER:  5√2 + 2√10

Answer 2

The denominator does seem quite weird, so why don't we just multiply it with its conjugate, (√5) + 2. But if we multiply the denominator, we have to multiply the numerator as well. In the end, we have ((√50) + 2(√10))

 

Of course, I'm assuming that you meant (√10)/((√5) - 2) and not (√10)/(√(5-2)). In the latter case, we simplify to get (√10)/(√3) or (√30)/3.