Simplify ( square root of 18x)÷( square root of 32)

$\sqrt{18 x} \div \sqrt{32}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{18 x}}{\sqrt{32}}$

Step 2

Combine $\sqrt{18 x}$ and $\sqrt{32}$ into a single radical.

$\sqrt{\frac{18 x}{32}}$

Step 3

Reduce the expression $\frac{18 x}{32}$ by cancelling the common factors.

Factor $2$ out of $18 x$ .

$\sqrt{\frac{2 (9 x)}{32}}$

Factor $2$ out of $32$ .

$\sqrt{\frac{2 (9 x)}{2 (16)}}$

Cancel the common factor.

$\sqrt{\frac{2 (9 x)}{2 \cdot 16}}$

Rewrite the expression.

$\sqrt{\frac{9 x}{16}}$

Step 4

Rewrite $\frac{9 x}{16}$ as ${(\frac{3}{4})}^{2} x$ .

Factor the perfect power $3^{2}$ out of $9 x$ .

$\sqrt{\frac{3^{2} x}{16}}$

Factor the perfect power $4^{2}$ out of $16$ .

$\sqrt{\frac{3^{2} x}{4^{2} \cdot 1}}$

Rearrange the fraction $\frac{3^{2} x}{4^{2} \cdot 1}$ .

$\sqrt{{(\frac{3}{4})}^{2} x}$

Step 5

Pull terms out from under the radical.

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

Step 6

Combine $\frac{3}{4}$ and $\sqrt{x}$ .

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