Algebra Examples

$\sqrt[5]{2 x} - \sqrt[5]{32 x^{5}} + \sqrt[5]{- 64 x} + \sqrt[3]{8 x^{3}}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $32 x^{5}$ as ${(2 x)}^{5}$ .

$\sqrt[5]{2 x} - \sqrt[5]{{(2 x)}^{5}} + \sqrt[5]{- 64 x} + \sqrt[3]{8 x^{3}}$

Step 1.2

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

$\sqrt[5]{2 x} - (2 x) + \sqrt[5]{- 64 x} + \sqrt[3]{8 x^{3}}$

Step 1.3

Multiply $2$ by $- 1$ .

$\sqrt[5]{2 x} - 2 x + \sqrt[5]{- 64 x} + \sqrt[3]{8 x^{3}}$

Step 1.4

Rewrite $- 64 x$ as ${(- 2)}^{5} \cdot (2 x)$ .

Tap for more steps...

Step 1.4.1

Factor $- 32$ out of $- 64$ .

$\sqrt[5]{2 x} - 2 x + \sqrt[5]{- 32 (2) x} + \sqrt[3]{8 x^{3}}$

Step 1.4.2

Rewrite $- 32$ as ${(- 2)}^{5}$ .

$\sqrt[5]{2 x} - 2 x + \sqrt[5]{{(- 2)}^{5} \cdot 2 x} + \sqrt[3]{8 x^{3}}$

Step 1.4.3

Add parentheses.

$\sqrt[5]{2 x} - 2 x + \sqrt[5]{{(- 2)}^{5} \cdot (2 x)} + \sqrt[3]{8 x^{3}}$

Step 1.5

Pull terms out from under the radical.

$\sqrt[5]{2 x} - 2 x - 2 \sqrt[5]{2 x} + \sqrt[3]{8 x^{3}}$

Step 1.6

Rewrite $8 x^{3}$ as ${(2 x)}^{3}$ .

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

Step 1.7

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

$\sqrt[5]{2 x} - 2 x - 2 \sqrt[5]{2 x} + 2 x$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Combine the opposite terms in $\sqrt[5]{2 x} - 2 x - 2 \sqrt[5]{2 x} + 2 x$ .

Tap for more steps...

Step 2.1.1

Add $- 2 x$ and $2 x$ .

$\sqrt[5]{2 x} + 0 - 2 \sqrt[5]{2 x}$

Step 2.1.2

Add $\sqrt[5]{2 x}$ and $0$ .

$\sqrt[5]{2 x} - 2 \sqrt[5]{2 x}$

Step 2.2

Subtract $2 \sqrt[5]{2 x}$ from $\sqrt[5]{2 x}$ .

$- \sqrt[5]{2 x}$