Simplify ( square root of 300)/( square root of 6)

$\frac{\sqrt{300}}{\sqrt{6}}$

Step 1

Combine $\sqrt{300}$ and $\sqrt{6}$ into a single radical.

$\sqrt{\frac{300}{6}}$

Step 2

Divide $300$ by $6$ .

$\sqrt{50}$

Step 3

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2)}$

Rewrite $25$ as $5^{2}$ .

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

Step 4

Pull terms out from under the radical.

$5 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2}$

Decimal Form:

$7.07106781 \dots$