Hello, slevvio!

I don't think there is an easy way . . .

First, we mustsuspectthat is a square.

Then we let: .

. . where both arerationalnumbers.

Square both sides: .

. . and we have:. . a^2 + 2b^2) + 2ab\sqrt{2}" alt="9 + 4\sqrt{2} \;=\a^2 + 2b^2) + 2ab\sqrt{2}" />

These two numbers are equal if their corresponding coefficients are equal.

So we have: .

The second equation gives us: .

Substitute into the first equation: .

Multiply by

. . which factors: .

. . and has roots: .

Since must be rational and the original square root is positive,

. . the only acceptable root is: .

Therefore: .