Question

Simplify the following radical
Sqrt 126x^13

Answer 1

`\large\boxed{\sqrt{126x^(13)}=3x^6√(14x)}`

Explanation:

`Domain:\ x\geq0\\\\\sqrt{126x^(13)}=\sqrt{9\cdot14\cdot x^(12+1)}\\\\\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=\sqrt{9\cdot14\cdot x^(12)\cdot x^1}=\sqrt{9\cdot14\cdot x^(6\cdot2)\cdot x}\\\\\text{use}\ √(ab)=√(a)\cdot√(b)\ \text{and}\ (a^n)^m=a^(nm)\\\\=\sqrt9\cdot√(14)\cdot√((x^6)^2)\cdot√(x)\\\\\text{use}\ √(a^2)=a\ \text{for}\ a\geq0\\\\=3\cdot√(14)\cdot x^6\cdot√(x)=3x^6√(14x)`