Question

Simplify the radical
Sqrt 84x^7

Answer 1

`\large\boxed{√(84x^7)=2x^3√(21x)}`

Explanation:

`Domain:\ x\geq0\\\\√(84x^7)=\sqrt{4\cdot21\cdot x^(6+1)}\\\\\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=√(4\cdot21\cdot x^6\cdot x^1)\\\\\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=\sqrt4\cdot√(21)\cdot\sqrt{x^(3\cdot2)}\cdot√(x)\\\\\text{use}\ (a^n)^m=a^(nm)\\\\=2\cdot√(21)\cdot√((x^3)^2)\cdot√(x)\\\\\text{use}\ √(a^2)=a\ \text{for}\ a\geq0\\\\=2\cdot√(21)\cdot x^3\cdot√(x)=2x^3√(21x)`