Simplify ( square root of 400x)/( square root of 5x)

$\frac{\sqrt{400 x}}{\sqrt{5 x}}$

Step 1

Combine $\sqrt{400 x}$ and $\sqrt{5 x}$ into a single radical.

$\sqrt{\frac{400 x}{5 x}}$

Step 2

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

Factor $5$ out of $400 x$ .

$\sqrt{\frac{5 (80 x)}{5 x}}$

Factor $5$ out of $5 x$ .

$\sqrt{\frac{5 (80 x)}{5 (x)}}$

Cancel the common factor.

$\sqrt{\frac{5 (80 x)}{5 x}}$

Rewrite the expression.

$\sqrt{\frac{80 x}{x}}$

Step 3

Cancel the common factor of $x$ .

Cancel the common factor.

$\sqrt{\frac{80 x}{x}}$

Divide $80$ by $1$ .

$\sqrt{80}$

Step 4

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5)}$

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

$\sqrt{4^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$4 \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$