Surd (fraction)

[Elance]

 

[MarkFL]

What have you tried, so we know where you're stuck?

 

[pka]

First expand the denominator:
\((3-\sqrt2)^2=9-6\sqrt2+2=~?\)
Now rationalize.

 

[JeffM]

Although rationalization is intuitively the obvious way to go after expanding the denominator, equating coefficients is perhaps a more general method and, in this case, little more work in terms of computation than rationalization.

 

[Mohammad Hammad]

(23/49) + (17/49)(2^0.5)

 

[JeffM]

Yes, EXCEPT you were supposed to give the coefficients

[MATH]a = \dfrac{23}{49} \text { and } b = \dfrac{17}{49}.[/MATH]
The 2^(0.5) makes your answer technically wrong. You were asked to find the coefficients, which explains why equating coefficients is good idea: it keeps you from answering the wrong question.

Do you know what I mean by equating coefficients?

 

[lookagain]

(23/49) + (17/49)(2^0.5)

This is a different username than the username who made the original post.