Evaluate square root of 18/49

$\sqrt{\frac{18}{49}}$

Step 1

Rewrite $\sqrt{\frac{18}{49}}$ as $\frac{\sqrt{18}}{\sqrt{49}}$ .

$\frac{\sqrt{18}}{\sqrt{49}}$

Step 2

Simplify the numerator.

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\frac{\sqrt{9 (2)}}{\sqrt{49}}$

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

$\frac{\sqrt{3^{2} \cdot 2}}{\sqrt{49}}$

Pull terms out from under the radical.

$\frac{3 \sqrt{2}}{\sqrt{49}}$

Step 3

Simplify the denominator.

Rewrite $49$ as $7^{2}$ .

$\frac{3 \sqrt{2}}{\sqrt{7^{2}}}$

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

$\frac{3 \sqrt{2}}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{3 \sqrt{2}}{7}$

Decimal Form:

$0.60609152 \dots$