Algebra Examples

$\sqrt{5 x} + \sqrt[3]{81 x} - \sqrt{45 x} - \sqrt[3]{27 x}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $81 x$ as $3^{3} \cdot (3 x)$ .

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Step 1.1.1

Factor $27$ out of $81$ .

$\sqrt{5 x} + \sqrt[3]{27 (3) x} - \sqrt{45 x} - \sqrt[3]{27 x}$

Step 1.1.2

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

$\sqrt{5 x} + \sqrt[3]{3^{3} \cdot 3 x} - \sqrt{45 x} - \sqrt[3]{27 x}$

Step 1.1.3

Add parentheses.

$\sqrt{5 x} + \sqrt[3]{3^{3} \cdot (3 x)} - \sqrt{45 x} - \sqrt[3]{27 x}$

Step 1.2

Pull terms out from under the radical.

$\sqrt{5 x} + 3 \sqrt[3]{3 x} - \sqrt{45 x} - \sqrt[3]{27 x}$

Step 1.3

Rewrite $45 x$ as $3^{2} \cdot (5 x)$ .

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Step 1.3.1

Factor $9$ out of $45$ .

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

Step 1.3.2

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

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

Step 1.3.3

Add parentheses.

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Multiply $3$ by $- 1$ .

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

Step 1.6

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

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

Step 1.7

Pull terms out from under the radical.

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

Step 1.8

Multiply $3$ by $- 1$ .

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

Step 2

Subtract $3 \sqrt{5 x}$ from $\sqrt{5 x}$ .

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