Simplify square root of 600x^6y^3

$\sqrt{600 x^{6} y^{3}}$

Step 1

Rewrite $600 x^{6} y^{3}$ as ${(10 x^{3} y)}^{2} \cdot (6 y)$ .

Factor $100$ out of $600$ .

$\sqrt{100 (6) x^{6} y^{3}}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 6 x^{6} y^{3}}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\sqrt{10^{2} \cdot 6 {(x^{3})}^{2} y^{3}}$

Factor out $y^{2}$ .

$\sqrt{10^{2} \cdot 6 {(x^{3})}^{2} (y^{2} y)}$

Move $6$ .

$\sqrt{10^{2} {(x^{3})}^{2} y^{2} \cdot 6 y}$

Rewrite $10^{2} {(x^{3})}^{2} y^{2}$ as ${(10 x^{3} y)}^{2}$ .

$\sqrt{{(10 x^{3} y)}^{2} \cdot 6 y}$

Add parentheses.

$\sqrt{{(10 x^{3} y)}^{2} \cdot (6 y)}$

Step 2

Pull terms out from under the radical.

$10 x^{3} y \sqrt{6 y}$