Simplify ( square root of 400x^2y^6)/( square root of 5)

$\frac{\sqrt{400 x^{2} y^{6}}}{\sqrt{5}}$

Step 1

Combine $\sqrt{400 x^{2} y^{6}}$ and $\sqrt{5}$ into a single radical.

$\sqrt{\frac{400 x^{2} y^{6}}{5}}$

Step 2

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{400 x^{2} y^{6}}{5}$ by cancelling the common factors.

Factor $5$ out of $400 x^{2} y^{6}$ .

$\sqrt{\frac{5 (80 x^{2} y^{6})}{5}}$

Factor $5$ out of $5$ .

$\sqrt{\frac{5 (80 x^{2} y^{6})}{5 (1)}}$

Cancel the common factor.

$\sqrt{\frac{5 (80 x^{2} y^{6})}{5 \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{80 x^{2} y^{6}}{1}}$

Divide $80 x^{2} y^{6}$ by $1$ .

$\sqrt{80 x^{2} y^{6}}$

Step 3

Rewrite $80 x^{2} y^{6}$ as ${(4 x y^{3})}^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5) x^{2} y^{6}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 5 x^{2} y^{6}}$

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

$\sqrt{4^{2} \cdot 5 x^{2} {(y^{3})}^{2}}$

Move $5$ .

$\sqrt{4^{2} x^{2} {(y^{3})}^{2} \cdot 5}$

Rewrite $4^{2} x^{2} {(y^{3})}^{2}$ as ${(4 x y^{3})}^{2}$ .

$\sqrt{{(4 x y^{3})}^{2} \cdot 5}$

Step 4

Pull terms out from under the radical.

$4 x y^{3} \sqrt{5}$