# Math Help - help please its gobledegook

1. ## help please its gobledegook

81 to the 3/4 I know the answer is 27 but how

and

express square root of 2 over square root of 2 + 1 in the form a+bsquare root2, where a and b are integers

2. Originally Posted by mathsfool
81 to the 3/4 I know the answer is 27 but how

and

express square root of 2 over square root of 2 + 1 in the form a+bsquare root2, where a and b are integers
$81^{\frac34} = \left(3^4\right)^{\frac34} =\left( \left(3^4\right)^{\frac14}\right)^3 = 3^3 = 27$

3. Originally Posted by mathsfool
...

express square root of 2 over square root of 2 + 1 in the form a+bsquare root2, where a and b are integers
I hope you mean:

$\frac{\sqrt{2}}{\sqrt{2} + 1}$

If so:

$\frac{\sqrt{2}}{\sqrt{2} + 1}\cdot \frac{\sqrt{2} - 1}{\sqrt{2} - 1} = \frac{2-\sqrt{2}}{2-1} = 2-1\cdot \sqrt{2}$