Question

Simplify the radical sqrt 120 x^11

Answer 1

Answer:

$\large\boxed{\sqrt{120x^{11}}=2x^5\sqrt{30x}}$

Step-by-step explanation:

$Domain:\ x\geq0\\\\\sqrt{120x^{11}}=\sqrt{4\cdot30\cdot x^{10+1}}\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt{4\cdot30\cdot x^{10}\cdot x^1}=\sqrt{4\cdot30\cdot x^{5\cdot2}\cdot x}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{and}\ (a^n)^m=a^{nm}\\\\=\sqrt4\cdot\sqrt{30}\cdot\sqrt{(x^5)^2}\cdot\sqrt{x}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=2\cdot\sqrt{30}\cdot x^5\cdot\sqrt{x}=2x^5\sqrt{30x}$