Question

Sqrt 100x^3
Simplify the radical

Answer 1

`\large\boxed{√(100x^3)=10x√(x)}`

Explanation:

`Domain:\ x\geq0\\\\√(100x^3)=\sqrt{10^2x^(2+1)}\\\\\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=√(10^2\cdot x^2\cdot x^1)\\\\\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=√(10^2)\cdot√(x^2)\cdot√(x)\\\\\text{use}\ √(a^2)=a\ \text{for}\ a\geq0\\\\=10\cdot x\cdot√(x)=10x√(x)`