# Simplifying surds

• Mar 30th 2010, 01:54 AM
cozza
Simplifying surds
Hi,

Can these examples be simplified any futher or is there an easier way to write them?

a=5

e = $\displaystyle \sqrt{1-15/25} =\sqrt{2/5}$

a/e = $\displaystyle 5/\sqrt{2/5}$

ae = $\displaystyle 5\times\sqrt{2/5}$

Thanks, I find these really difficult (Headbang)
• Mar 30th 2010, 01:58 AM
HallsofIvy
Quote:

Originally Posted by cozza
Hi,

Can these examples be simplified any futher or is there an easier way to write them?

a=5

e = $\displaystyle \sqrt{1-15/25} =\sqrt{2/5}$

a/e = $\displaystyle 5/\sqrt{2/5}$

You can "rationalize the denominator": multiply both numerator and denominator to get $\displaystyle \frac{5\sqrt{2/5}}{2/5}= \frac{25\sqrt{2/5}}{2}$

Quote:

ae = $\displaystyle 5\times\sqrt{2/5}$

Thanks, I find these really difficult (Headbang)
• Mar 30th 2010, 02:02 AM
Stroodle
Hi there.

$\displaystyle \sqrt{1-\frac{15}{25}}=\sqrt{\frac{10}{25}}=\frac{\sqrt{10 }}{\sqrt{25}}=\frac{\sqrt{10}}{5}$

so,

$\displaystyle 5\div \frac{\sqrt{10}}{5}=5\times\frac{5}{\sqrt{10}}=\fr ac{25}{\sqrt{10}}=\frac{25\sqrt{10}}{10}=\frac{5\s qrt{10}}{2}$

and

$\displaystyle 5\times\frac{\sqrt{10}}{5}=\sqrt{10}$