Question

what is the expression in simplest radical form?
√432
enter your answer in the box.

Explanation:

Step1: Prime - factorize 432

$432=2\times216 = 2\times2\times108=2\times2\times2\times54 = 2\times2\times2\times2\times27=2^4\times3^3$

Step2: Apply square - root property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$

$\sqrt{432}=\sqrt{2^4\times3^3}=\sqrt{2^4}\cdot\sqrt{3^3}$

Step3: Simplify each square - root

$\sqrt{2^4}=2^2 = 4$, and $\sqrt{3^3}=\sqrt{3^2\times3}=3\sqrt{3}$

Step4: Multiply the simplified square - roots

$4\times3\sqrt{3}=12\sqrt{3}$

Answer:

$12\sqrt{3}$