Simplify the Radical Expression ( square root of 27)/( square root of 48)

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

Step 1

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

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

Step 2

Cancel the common factor of $27$ and $48$ .

Factor $3$ out of $27$ .

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

Cancel the common factors.

Factor $3$ out of $48$ .

$\sqrt{\frac{3 \cdot 9}{3 \cdot 16}}$

Cancel the common factor.

$\sqrt{\frac{3 \cdot 9}{3 \cdot 16}}$

Rewrite the expression.

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

Step 3

Rewrite $\sqrt{\frac{9}{16}}$ as $\frac{\sqrt{9}}{\sqrt{16}}$ .

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

Step 4

Simplify the numerator.

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

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

Pull terms out from under the radical.

$\frac{| 3 |}{\sqrt{16}}$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$\frac{3}{\sqrt{16}}$

Step 5

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

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

Pull terms out from under the radical.

$\frac{3}{| 4 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$\frac{3}{4}$