# How do you simplify \sqrt{36-4x^{2}}?

Jan 11, 2018

$\sqrt{36 - 4 {x}^{2}} = 2 \sqrt{\left(3 - x\right) \left(3 + x\right)}$

#### Explanation:

$\sqrt{36 - 4 {x}^{2}} = 2 \sqrt{\left(3 - x\right) \left(3 + x\right)}$

because:

$36 - 4 {x}^{2} = 4 \left(9 - {x}^{2}\right) = 4 \left({3}^{2} - {x}^{2}\right) = 4 \left(3 - x\right) \left(3 + x\right) = - 4 \left(x - 3\right) \left(x + 3\right)$

As a result :

$\sqrt{36 - 4 {x}^{2}} = \sqrt{4 \left(3 - x\right) \left(3 + x\right)} = \sqrt{4} \cdot \sqrt{\left(3 - x\right) \left(3 + x\right)} = 2 \sqrt{\left(3 - x\right) \left(3 + x\right)}$

Jan 11, 2018

$2 \sqrt{\left(3 - x\right) \left(3 + x\right)}$

#### Explanation:

$\text{factorise the radicand}$

$36 - 4 {x}^{2} = 4 \left(9 - {x}^{2}\right) \leftarrow \textcolor{b l u e}{\text{common factor of 4}}$

$9 - {x}^{2} \text{ is a "color(blue)"difference of squares}$

•color(white)(x)a^2-b^2=(a-b)(a+b)

$9 - {x}^{2} = {3}^{2} - {x}^{2} = \left(3 - x\right) \left(3 + x\right)$

$\Rightarrow \sqrt{36 - 4 {x}^{2}}$

$= \sqrt{4 \left(x - 3\right) \left(x + 3\right)}$

$= 2 \sqrt{\left(x - 3\right) \left(x + 3\right)}$