# INTRODUCTION TO SURDS (SIMPLICATION OF SURD)

Some numbers, as you know, cannot be written in exact fractions. An example is 3.432. These are called irrational numbers

A kind of irrational number is surd. Surd is a square root that can not be written in an exact fraction.

For example, $\sqrt{7}$ is a surd as it can not be written in exact fraction.

Sometimes, it may be necessary to simplify surd or express the number under the square root as a product of two factors, where one factor is a perfect square and another rational number. This is called the simplification of surds.

Simplification of surd simply means we should express a surd in its basic form.

The accompanying example will show you how to simplify surds.

But before then, here is one thing you should know:

$\sqrt{xy}=\sqrt{x}\times\sqrt{y}$

Example 1
Simplify $\sqrt{90}$

Solution
$\sqrt{90}=\sqrt{9\times10}$
$\sqrt{90}=\sqrt{9}\times\sqrt{10}$
$=3\sqrt{10}$

Example 2
Simplify $\sqrt{294}$

Solution
$\sqrt{294}=\sqrt{49\times6}$
$\sqrt{294}=\sqrt{49}\times\sqrt{6}$
$=7\sqrt{6}$

Example 3
Simplify $\sqrt{700}$

Solution
$\sqrt{294}=\sqrt{100\times7}$
$\sqrt{294}=\sqrt{100}\times\sqrt{7}$
$=10\sqrt{7}$

Example 4
Simplify $\sqrt{9800}$

Solution
$\sqrt{9800}=\sqrt{4900\times2}$
$\sqrt{9800}=\sqrt{4900}\times\sqrt{2}$
$=70\sqrt{2}$

Example 5
Simplify $\sqrt{512}$

Solution
$\sqrt{512}=\sqrt{256\times2}$
$\sqrt{512}=\sqrt{256}\times\sqrt{2}$
$=16\sqrt{2}$

Example 6
Simplify $\sqrt{1152}$

Solution
$\sqrt{1152}=\sqrt{576\times2}$
$\sqrt{1152}=\sqrt{576}\times\sqrt{2}$
$=24\sqrt{2}$

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Example 7
Simplify $\sqrt{800}$

Solution
$\sqrt{800}=\sqrt{100\times8}$
$\sqrt{800}=\sqrt{100}\times\sqrt{8}$
$=10\sqrt{8}$

We've learned how to simplify surd. In the following post, we'll be adding and subtracting surds.

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