Algebra Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite

$27$ as

$3^{2} \cdot 3$ .

Tap for more steps...

Step 1.1.1

Factor

$9$ out of

$27$ .

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

Step 1.1.2

Rewrite

$9$ as

$3^{2}$ .

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Multiply

$3$ by

$5$ .

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

Step 1.4

Rewrite

$27$ as

$3^{3}$ .

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

Step 1.5

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

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

Step 1.6

Multiply

$- 2$ by

$3$ .

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

Step 1.7

Rewrite

$27$ as

$3^{3}$ .

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

Step 1.8

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

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

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:

$22.98076211 \dots$