How 1 2 can be equal to 2 2 ?

Question

How       1          2        can be equal to             2        2  ?

noruegezajl00y · Accepted Answer

Since   2  =      2    ⋅      2   you have that            2        2    =            2                      2                    2              =      1          2

lasquiyas5loaa · Accepted Answer

One thing we tend to like to do when dealing with this stuff is have the denominator of fractionish things as a plain number, as much as possible. To do this, we'll multiply both top and bottom by something that will cancel out any radicals in the bottom.

\sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} = \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}

This even works for more complicated stuff.

\frac{1}{\sqrt{5} + \sqrt{3}} = \frac{1}{\sqrt{5} + \sqrt{3}} \cdot \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}} = \frac{\sqrt{5} - \sqrt{3}}{5 - 3} = \frac{\sqrt{5} - \sqrt{3}}{2}

How 1 <msqrt> 2 </msqrt> </mfrac> can be equal to <msqrt>

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