# How do you simplify sqrt(432)?

Aug 20, 2016

$\sqrt{432} = 12 \sqrt{3}$

#### Explanation:

$432 = {2}^{4} \cdot {3}^{3} = 2 \cdot 2 \cdot 3 \cdot 2 \cdot 2 \cdot 3 \cdot 3 = {12}^{2} \cdot 3$

So we find:

$\sqrt{432} = \sqrt{{12}^{2} \cdot 3} = \sqrt{{12}^{2}} \cdot \sqrt{3} = 12 \sqrt{3}$

Aug 20, 2016

$12 \sqrt{3}$

#### Explanation:

Let us factorize given the number $432$. For an even number $2$ is a factor

$\frac{432}{2} = 216$
$\frac{216}{2} = 108$
$\frac{108}{2} = 54$
$\frac{54}{2} = 27$
we observe that $3$ is a factor
$\frac{27}{3} = 9$
$\frac{9}{3} = 3$
$\therefore 432 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3$
$\implies \sqrt{432} = \sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3}$
paring and taking one digit for each pair out of the square root sign we get
$\sqrt{432} = \sqrt{\overline{2 \times 2} \times \overline{2 \times 2} \times \overline{3 \times 3} \times 3}$
$\implies \sqrt{432} = 2 \times 2 \times 3 \sqrt{3}$
$\implies \sqrt{432} = 12 \sqrt{3}$