Simplify the Radical Expression square root of 27/16

$\sqrt{\frac{27}{16}}$

Rewrite $\sqrt{\frac{27}{16}}$ as $\frac{\sqrt{27}}{\sqrt{16}}$ .

$\frac{\sqrt{27}}{\sqrt{16}}$

Simplify the numerator.

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

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

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

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

Pull terms out from under the radical.

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

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

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

Simplify the denominator.

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

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

Pull terms out from under the radical.

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

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.29903810 \dots$