Question

Simplify the radical sqrt 120 x^11

Answer 1

`\large\boxed{\sqrt{120x^(11)}=2x^5√(30x)}`

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}\ √(ab)=√(a)\cdot√(b)\ \text{and}\ (a^n)^m=a^(nm)\\\\=\sqrt4\cdot√(30)\cdot√((x^5)^2)\cdot√(x)\\\\\text{use}\ √(a^2)=a\ \text{for}\ a\geq0\\\\=2\cdot√(30)\cdot x^5\cdot√(x)=2x^5√(30x)`