How do I simplify to ?
Thanks
Hello, slevvio!
I don't think there is an easy way . . .
First, we must suspect that is a square.
Then we let: .
. . where both are rational numbers.
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: .