How do you rationalize 3 / (sqrt5 -sqrt2) 352?

1 Answer
May 14, 2015

You can rationalize the denominator by multiplying top and bottom by the conjugate sqrt(5) + sqrt(2)5+2 as follows:

3/(sqrt(5)-sqrt(2))352

= (3*(sqrt(5)+sqrt(2)))/((sqrt(5)-sqrt(2))(sqrt(5)+sqrt(2))=3(5+2)(52)(5+2)

= (3*(sqrt(5)+sqrt(2)))/(sqrt(5)sqrt(5)-sqrt(2)sqrt(2))=3(5+2)5522

= (3*(sqrt(5)+sqrt(2)))/(5-2)=3(5+2)52

= (3*(sqrt(5)+sqrt(2)))/3=3(5+2)3

= sqrt(5)+sqrt(2)=5+2