Question

Which ecpression is equivalent to sqrt 8x^7y^8?

Answer 1

c is correct

Explanation:

edge 2020

Answer 2

`Domain:\ x\geq0\ \wedge\ y\in\mathbb{R}`

`√(8x^7y^8)=\sqrt8\cdot√(x^7)\cdot√(y^8)=√(4\cdot2)\cdot√(x^6\cdot x)\cdot\sqrt{y^(4\cdot2)}\\\\=\sqrt4\cdot\sqrt2\cdot√(x^6)\cdot√(x)\cdot√((y^4)^2)=2\sqrt2\cdot\sqrt{x^(3\cdot2)}\cdot√(x)\cdot y^4\\\\=2y^4\sqrt2\cdot√((x^3)^2)\cdot√(x)=2y^4√(2x)\cdot x^3\\\\=\boxed{2x^3y^4√(2x)}`

`Used:\\\\√(ab)=√(a)\cdot√(b)\\\\√(a^2)=a\ for\ a\geq0`