Question

how to simplify radical

Answer 1

\(\large {
\sqrt{12x^9}-3x^2\sqrt{3x^5}\qquad
\begin{cases}
12\to 3\cdot 2\cdot 2\to 3\cdot 2^2
\\ \quad \\

x^9\to x^{2+2+2+2+1}\to x^{8+1}\to x^8\cdot x^1
\\ \quad

\qquad (x^4)^2\cdot x\\
x^5\to x^{2+2+1}\to x^{4+1}\to x^4\cdot x^1\\
\qquad (x^2)^2\cdot x
\end{cases}\qquad thus
\\ \quad \\
\sqrt{12x^9}-3x^2\sqrt{3x^5}\implies \sqrt{ 3\cdot 2^2\cdot (x^4)^2\cdot x}-3x^2\sqrt{3\cdot (x^2)^2\cdot x}
}\)

take out what you can out of the radical
see what you end up with