Question

Simplify the following radical sqrt 300 x^15

Answer 1

Answer:

$\large\boxed{\sqrt{300x^{15}}=10x^7\sqrt{3x}}$

Step-by-step explanation:

$Domain: x\geq0\\\\\sqrt{300x^{15}}=\sqrt{100\cdot3\cdot x^{14+1}}\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt{100\cdot3\cdot x^{14}\cdot x^1}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{100}\cdot\sqrt3\cdot\sqrt{x^{14}}\cdot\sqrt{x}=10\cdot\sqrt3\cdot\sqrt{x^{7\cdot2}}\cdot\sqrt{x}\\\\\text{use}\ (a^n)^m=a^{nm}\\\\=10\cdot\sqrt3\cdot\sqrt{(x^7)^2}\cdot\sqrt{x}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=10\cdot\sqrt3\cdot x^7\cdot\sqrt{x}=10x^7\sqrt{3x}$