Rationalise the deneminato \( \frac{1+2 \sqrt{2}}{\sqrt[1]{4}} \)

To rationalize the denominator of the expression \( \frac{1 + 2 \sqrt{2}}{\sqrt{4}} \), first, simplify the denominator, which is \( \sqrt{4} = 2 \). This leads to the expression \( \frac{1 + 2 \sqrt{2}}{2} \). Next, we can separate the numerator by dividing both terms: \[ \frac{1}{2} + \frac{2 \sqrt{2}}{2} = \frac{1}{2} + \sqrt{2}. \] So, the final simplified expression is: \[ \frac{1}{2} + \sqrt{2}. \]