Question

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

Answer 1

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

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

$Used:\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=a\ for\ a\geq0$