Simplify the Radical Expression 5 square root of 27-2 cube root of 27+ cube root of 27

$5 \sqrt{27} - 2 \sqrt[3]{27} + \sqrt[3]{27}$

Step 1

Simplify each term.

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

Factor $9$ out of $27$ .

$5 \sqrt{9 (3)} - 2 \sqrt[3]{27} + \sqrt[3]{27}$

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

$5 \sqrt{3^{2} \cdot 3} - 2 \sqrt[3]{27} + \sqrt[3]{27}$

Pull terms out from under the radical.

$5 (| 3 | \sqrt{3}) - 2 \sqrt[3]{27} + \sqrt[3]{27}$

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

$5 (3 \sqrt{3}) - 2 \sqrt[3]{27} + \sqrt[3]{27}$

Multiply $3$ by $5$ .

$15 \sqrt{3} - 2 \sqrt[3]{27} + \sqrt[3]{27}$

Rewrite $27$ as $3^{3}$ .

$15 \sqrt{3} - 2 \sqrt[3]{3^{3}} + \sqrt[3]{27}$

Pull terms out from under the radical.

$15 \sqrt{3} - 2 \cdot 3 + \sqrt[3]{27}$

Multiply $- 2$ by $3$ .

$15 \sqrt{3} - 6 + \sqrt[3]{27}$

Rewrite $27$ as $3^{3}$ .

$15 \sqrt{3} - 6 + \sqrt[3]{3^{3}}$

Pull terms out from under the radical.

$15 \sqrt{3} - 6 + 3$

Step 2

Add $- 6$ and $3$ .

$15 \sqrt{3} - 3$

Step 3

The result can be shown in multiple forms.

Exact Form:

$15 \sqrt{3} - 3$

Decimal Form:

$22.98076211 \dots$