**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 a**² - 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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