Simplify ( square root of 27x)÷( square root of 48)

$\sqrt{27 x} \div \sqrt{48}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{27 x}}{\sqrt{48}}$

Step 2

Combine $\sqrt{27 x}$ and $\sqrt{48}$ into a single radical.

$\sqrt{\frac{27 x}{48}}$

Step 3

Reduce the expression $\frac{27 x}{48}$ by cancelling the common factors.

Factor $3$ out of $27 x$ .

$\sqrt{\frac{3 (9 x)}{48}}$

Factor $3$ out of $48$ .

$\sqrt{\frac{3 (9 x)}{3 (16)}}$

Cancel the common factor.

$\sqrt{\frac{3 (9 x)}{3 \cdot 16}}$

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 $\sqrt{x}$ .

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