Evaluate square root of 5/9- square root of 5/36

$\sqrt{\frac{5}{9}} - \sqrt{\frac{5}{36}}$

Step 1

Simplify each term.

Rewrite $\sqrt{\frac{5}{9}}$ as $\frac{\sqrt{5}}{\sqrt{9}}$ .

$\frac{\sqrt{5}}{\sqrt{9}} - \sqrt{\frac{5}{36}}$

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{5}}{\sqrt{3^{2}}} - \sqrt{\frac{5}{36}}$

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

$\frac{\sqrt{5}}{3} - \sqrt{\frac{5}{36}}$

Rewrite $\sqrt{\frac{5}{36}}$ as $\frac{\sqrt{5}}{\sqrt{36}}$ .

$\frac{\sqrt{5}}{3} - \frac{\sqrt{5}}{\sqrt{36}}$

Simplify the denominator.

Rewrite $36$ as $6^{2}$ .

$\frac{\sqrt{5}}{3} - \frac{\sqrt{5}}{\sqrt{6^{2}}}$

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

$\frac{\sqrt{5}}{3} - \frac{\sqrt{5}}{6}$

Step 2

To write $\frac{\sqrt{5}}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\sqrt{5}}{3} \cdot \frac{2}{2} - \frac{\sqrt{5}}{6}$

Step 3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{\sqrt{5}}{3}$ by $\frac{2}{2}$ .

$\frac{\sqrt{5} \cdot 2}{3 \cdot 2} - \frac{\sqrt{5}}{6}$

Multiply $3$ by $2$ .

$\frac{\sqrt{5} \cdot 2}{6} - \frac{\sqrt{5}}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{\sqrt{5} \cdot 2 - \sqrt{5}}{6}$

Step 5

Simplify the numerator.

Move $2$ to the left of $\sqrt{5}$ .

$\frac{2 \cdot \sqrt{5} - \sqrt{5}}{6}$

Subtract $\sqrt{5}$ from $2 \sqrt{5}$ .

$\frac{\sqrt{5}}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{5}}{6}$

Decimal Form:

$0.37267799 \dots$