Question

What is $\sqrt{192}$ in simplest radical form?

Answer 1

$\sqrt{192}=8\sqrt{3}$

Explanation:

Your answer is correct. Here's why....

If $a,b\ge 0$ then:

$\sqrt{ab}=\sqrt{a}\sqrt{b}$

If $a\ge 0$ then:

$\sqrt{a^2}=a$

Find the prime factorization of $192$ and identify square factors:

$192=\mathrm{2.2.2.2.2.2.3}=2^6.3=(2^3{)}^2.3=8^2.3$

So:

$\sqrt{192}=\sqrt{8^2.3}=\sqrt{8^2}.\sqrt{3}=8\sqrt{3}$