DIVISION OF SURDS

Post a Comment
As is with numbers, surds can also be divided.

The rule is this:
$\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$

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

Solution: 
$\frac{\sqrt{72}}{\sqrt{8}}=\sqrt{\frac{72}{8}}$
$\sqrt{\frac{72}{8}}=\sqrt{9}$
$\sqrt{9}=3$

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

Solution:
$\frac{\sqrt{192}}{\sqrt{3}}$ can be written as $\sqrt{\frac{192}{3}}$
$\sqrt{\frac{192}{3}}=\sqrt{64}$
$\sqrt{64}=8$

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

Solution:
$\frac{\sqrt{3}\times\require{cancel}\bcancel{\sqrt{18}}}{\require{cancel}\bcancel{\sqrt{18}}}$ 
$\sqrt{3}$

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 $\frac{12}{\sqrt{6}}$

Solution
Rationalizing the denominator
$\frac{12}{\sqrt{6}}\times\frac{\sqrt{6}}{\sqrt{6}}$
$\frac{12\sqrt{6}}{\sqrt{36}}$
$\frac{12\sqrt{6}}{6}$

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

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 ($2\sqrt{6}$).

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

Solution
$\sqrt{12}$ can be simplified further, hence
$\frac{20\sqrt{2}}{\sqrt{4\times3}}$
$\frac{20\sqrt{2}}{2\sqrt{3}}$

Now, let's rationalize the denominator
$\frac{20\sqrt{2}}{2\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}$
$\frac{20\sqrt{6}}{2\sqrt{9}}$
$\frac{20\sqrt{6}}{2(3)}$
$\frac{20\sqrt{6}}{6}$
$\frac{10\sqrt{6}}{3}$

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.
Help us grow our readership by sharing this post

Related Posts

Post a Comment

Subscribe Our Newsletter