Simplify the Radical Expression square root of 3^5

$\sqrt{3^{5}}$

Step 1

Raise $3$ to the power of $5$ .

$\sqrt{243}$

Step 2

Rewrite $243$ as $9^{2} \cdot 3$ .

Factor $81$ out of $243$ .

$\sqrt{81 (3)}$

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2} \cdot 3}$

Step 3

Pull terms out from under the radical.

$| 9 | \sqrt{3}$

Step 4

The absolute value is the distance between a number and zero. The distance between $0$ and $9$ is $9$ .

$9 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{3}$

Decimal Form:

$15.58845726 \dots$