# HOW TO FIND THE SQUARE ROOT OF A QUADRATIC EQUATION

## About "How to find the square root of a quadratic equation"

How to find the square root of a quadratic equation :

To find the square root of a quadratic equation, we use one of the following methods.

• Converting the given equation in the form of a² + 2ab + b² (or) a² - 2ab + b²
• Factoring
• long division

Let us see some examples to understand the above concepts.

Note : In all ways we will get the same answer.

Example 1 :

Find the square root of the following quadratic equation

x² - 22 x + 121

Solution :

To find the square root of the quadratic equation x² - 22 x + 121, first let us try to write the given equation in the form of a² - 2ab + b².For that we have to split the second terms that is 22x and the multiple of 2.

=  √x² - 22 x + 121

=  √(x² - 2 x (11) + 11²)

=  √(x + 11)(x + 11)

=  |x + 11|

Hence the square root of x² - 22 x + 121 is |x + 11|.

Example 2 :

Find the square root of the following quadratic equation

4x² - 12 x + 9

Solution :

Let us use the second method that is factoring to find the square root of the above equation.

=  4x² - 12 x + 9

=  4x² - 6 x - 6 x  + 9

=  2x (2x - 3) - 3(2x - 3)

=  (2x - 3) (2x - 3)

√(4x² - 12 x + 9 )  =  (2x - 3) (2x - 3)  =  |2x - 3|

Example 3 :

Find the square root of the following quadratic equation

4x² - 4 x + 1

Solution :

Let us use the third method that is long division to find the square root of the above equation.

=  4x² - 4 x + 1

Step 1 :

Split the first term 4x² as the multiple of two same terms. That us , 4x² = 2x (2x)

Step 2 :

Multiply the numerator by 2

Step 3 :

Divide the new term that is 4x by the second term of the given quadratic equation.

4x/(-4x) = -1

4x² - 4 x + 1  =   |2x - 1|

After having gone through the stuff given above, we hope that the students would have understood "How to find the square root of a quadratic equation".

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