Evaluate ( square root of 2)/( square root of 50)

$\frac{\sqrt{2}}{\sqrt{50}}$

Step 1

Combine $\sqrt{2}$ and $\sqrt{50}$ into a single radical.

$\sqrt{\frac{2}{50}}$

Step 2

Cancel the common factor of $2$ and $50$ .

Factor $2$ out of $2$ .

$\sqrt{\frac{2 (1)}{50}}$

Cancel the common factors.

Factor $2$ out of $50$ .

$\sqrt{\frac{2 \cdot 1}{2 \cdot 25}}$

Cancel the common factor.

$\sqrt{\frac{2 \cdot 1}{2 \cdot 25}}$

Rewrite the expression.

$\sqrt{\frac{1}{25}}$

Step 3

Rewrite $\sqrt{\frac{1}{25}}$ as $\frac{\sqrt{1}}{\sqrt{25}}$ .

$\frac{\sqrt{1}}{\sqrt{25}}$

Step 4

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{25}}$

Step 5

Simplify the denominator.

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

$\frac{1}{\sqrt{5^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{1}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5}$

Decimal Form:

$0.2$