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As is with numbers, surds can also be divided.

The rule is this:

Example 1
Simplify $\frac{\sqrt{72}}{\sqrt{8}}$


Example 2
Simplify $\frac{\sqrt{192}}{\sqrt{3}}$

$\frac{\sqrt{192}}{\sqrt{3}}$ can be written as $\sqrt{\frac{192}{3}}$

Example 3
Write $\frac{\sqrt{3}\times\sqrt{18}}{\sqrt{18}}$ in the simplest form possible.


In some cases, you may need to rationalize the surd. Rationalizing the surd is the processing of removing the irrational number from the denominator of the surd. 

To rationalize a surd, you quickly multiply the denominator and numerator by the conjugates of the denominator so that the denominator becomes a rational number

Example 4
By rationalizing the denominator, simplify $\frac{12}{\sqrt{6}}$

Rationalizing the denominator

If $\frac{12}{6}=2$, then

Note: the multiplication of $\frac{\sqrt{6}}{\sqrt{6}}$ is equivalent to multiplication by $1$. Hence the value of the given fraction($\frac{12}{\sqrt{6}})$ correspond with our derived answer ($2\sqrt{6}$).

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Example 5
By Rationalizing the denominator, write $\frac{20\sqrt{2}}{\sqrt{12}}$ in the simplest form possible.

$\sqrt{12}$ can be simplified further, hence

Now, let's rationalize the denominator

That is all for now. We would be concluding our series on surds in this next post. We would expect your question in our telegram community.
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