help please its gobledegook

**mathsfool** · September 22nd 2008, 11:54 AM

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

**earboth** · September 22nd 2008, 11:59 AM

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

$81^{\frac34} = \left(3^4\right)^{\frac34} =\left( \left(3^4\right)^{\frac14}\right)^3 = 3^3 = 27$

**earboth** · September 22nd 2008, 12:03 PM

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:

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

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