Evaluate ( square root of 48)/( square root of 27)

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

Step 1

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

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

Step 2

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

Factor $3$ out of $48$ .

$\sqrt{\frac{3 (16)}{27}}$

Cancel the common factors.

Factor $3$ out of $27$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

Simplify the numerator.

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

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

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

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

Step 5

Simplify the denominator.

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

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

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

$\frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$