Question

What is 3 square root 72 in simplest radical form?
I got 3 square root 4. But I'm bad at radicals
Is this correct?

Answer 1

\[18\sqrt{2}\]

Answer 2

\(\sqrt 4 = 2\), so a simplified root cannot contain \(\sqrt 4\).
Also, if answer that \(3\sqrt {72} = 3\sqrt 4 \) then you are stating that \(\sqrt {72} = \sqrt 4 \), which is not true.

You need to factor out the largest perfect square there is.
\(72 = 36 \times 2\), and \(\sqrt {36} = 6\)

\(3 \sqrt{72} = 3\sqrt {36 \times 2} = 3\sqrt{36}\sqrt 2 = 3 \times 6 \sqrt 2 = 18 \sqrt 2\)