Question

Simplify the following sqrt 120x^15

Answer 1

`\large\boxed{\sqrt{120x^(15)}=2x^7√(30x)}`

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}\ √(ab)=√(a)\cdot√(b)\\\\=\sqrt4\cdot√(30)\cdot\sqrt{x^(14)}\cdot√(x)=2\cdot√(30)\cdot\sqrt{x^(7\cdot2)}\cdot√(x)\\\\\text{use}\ (a^n)^m=a^(nm)\\\\=2\cdot√(30)\cdot√((x^7)^2)\cdot√(x)\\\\\text{use}\ √(a^2)=a\ \text{for}\ a\geq0\\\\=2\cdot√(30)\cdot x^7\cdot√(x)=2x^7√(30x)`