Simplify ( square root of 18)/( square root of 8)

$\frac{\sqrt{18}}{\sqrt{8}}$

Step 1

Combine $\sqrt{18}$ and $\sqrt{8}$ into a single radical.

$\sqrt{\frac{18}{8}}$

Step 2

Cancel the common factor of $18$ and $8$ .

Factor $2$ out of $18$ .

$\sqrt{\frac{2 (9)}{8}}$

Cancel the common factors.

Factor $2$ out of $8$ .

$\sqrt{\frac{2 \cdot 9}{2 \cdot 4}}$

Cancel the common factor.

$\sqrt{\frac{2 \cdot 9}{2 \cdot 4}}$

Rewrite the expression.

$\sqrt{\frac{9}{4}}$

Step 3

Rewrite $\sqrt{\frac{9}{4}}$ as $\frac{\sqrt{9}}{\sqrt{4}}$ .

$\frac{\sqrt{9}}{\sqrt{4}}$

Step 4

Simplify the numerator.

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

$\frac{\sqrt{3^{2}}}{\sqrt{4}}$

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

$\frac{3}{\sqrt{4}}$

Step 5

Simplify the denominator.

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

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

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

$\frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$