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Today's #topic

**SURDS**

Numbers like **2**,**2.4**,**0.3**.**0.6**,**√64** can be expressed as exact fractions or ratios:**5/1**,**1/3** ,**3/5**,**8** . These are rational numbers.

But Numbers that cannot be written in ratio form are known as irrational numbers.

For example **π= 3.1415........,

Other example of irrational numbers are **√5= 2.236067977...,** and **√7 = 2.645751....,**

Numbers that are irrational are called **SURD**.

Two or more surd are called surds if the numbers under square root sign and the same, for example **√5 , 3√3 , √3/2 are called surds.

# Simplification of surds

To simplify a surd, where possible, Express the number under the square root sign as a product of two factors, one which is a perfect square.

Then simplify the surd by taking the square root of the perfect square.

**EXAMPLE 1**

To simplify √20

**step **

Express the number under the square root sign as a product of two factors as in

**√20= √4x√5**

then simplify

**√20= 2x√5**

**=2√5**

**EXAMPLE 2**

To simplify **3√50**

**step**

Express the number under the square root sign as a product of two factors as in

**3√50= 3x√25x√2**

Notice that this is more complex than the first one

You should not be confused by the **3**. It is just multiplied by the **√50**.

So you can just solve that of **√50** and multiplied by **3**

**3√50= 3x5x√2**

**=15√2**

YOU CAN ASK ANY QUESTION IN THE COMMENT SECTION

**SOLVE THIS QUESTION IN THE COMMENT SESSION**

SIMPLIFY THE FOLLOWING

1, **√162**

2, **√1000**

3, **2√500**

CORRECT ANSWER WILL BE UPVOTED