Question

Simplify the following sqrt 120x^15

Answer 1

Answer:

$\large\boxed{\sqrt{120x^{15}}=2x^7\sqrt{30x}}$

Step-by-step explanation:

$Domain:\ x\geq0\\\\\sqrt{120x^{15}}=\sqrt{4\cdot30\cdot x^{14+1}}\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt{4\cdot30\cdot x^{14}\cdot x^1}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt4\cdot\sqrt{30}\cdot\sqrt{x^{14}}\cdot\sqrt{x}=2\cdot\sqrt{30}\cdot\sqrt{x^{7\cdot2}}\cdot\sqrt{x}\\\\\text{use}\ (a^n)^m=a^{nm}\\\\=2\cdot\sqrt{30}\cdot\sqrt{(x^7)^2}\cdot\sqrt{x}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=2\cdot\sqrt{30}\cdot x^7\cdot\sqrt{x}=2x^7\sqrt{30x}$