How does

(3√2)/6 - (8√2)/216 = (100√2)/216 ?

Thanks

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- Feb 18th 2010, 07:23 AMCSG18Fractions
How does

(3√2)/6 - (8√2)/216 = (100√2)/216 ?

Thanks - Feb 18th 2010, 07:44 AMe^(i*pi)
The LCD of 6 and 216 is 216.

Multiply the first term by 36/36

$\displaystyle \frac{36}{36} \cdot \frac{3\sqrt{2}}{6} = \frac{108 \sqrt2}{216}$

Now they have the same denominator they can be combined

$\displaystyle \frac{108 \sqrt{2} - 8 \sqrt{2}}{216}$

Factor out $\displaystyle \sqrt{2}$

$\displaystyle \frac{\sqrt{2}(108-8)}{216} = \frac{100\sqrt2}{216}$

This equals the RHS but since both numerator and denominator are multiples of 4 we can cancel it down to $\displaystyle \frac{25 \sqrt{2}}{54}$