Algebra Examples

$\sqrt[3]{250} + \sqrt[3]{54} + \sqrt{72}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $250$ as $5^{3} \cdot 2$ .

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Step 1.1.1

Factor $125$ out of $250$ .

$\sqrt[3]{125 (2)} + \sqrt[3]{54} + \sqrt{72}$

Step 1.1.2

Rewrite $125$ as $5^{3}$ .

$\sqrt[3]{5^{3} \cdot 2} + \sqrt[3]{54} + \sqrt{72}$

Step 1.2

Pull terms out from under the radical.

$5 \sqrt[3]{2} + \sqrt[3]{54} + \sqrt{72}$

Step 1.3

Rewrite $54$ as $3^{3} \cdot 2$ .

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Step 1.3.1

Factor $27$ out of $54$ .

$5 \sqrt[3]{2} + \sqrt[3]{27 (2)} + \sqrt{72}$

Step 1.3.2

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

$5 \sqrt[3]{2} + \sqrt[3]{3^{3} \cdot 2} + \sqrt{72}$

Step 1.4

Pull terms out from under the radical.

$5 \sqrt[3]{2} + 3 \sqrt[3]{2} + \sqrt{72}$

Step 1.5

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 1.5.1

Factor $36$ out of $72$ .

$5 \sqrt[3]{2} + 3 \sqrt[3]{2} + \sqrt{36 (2)}$

Step 1.5.2

Rewrite $36$ as $6^{2}$ .

$5 \sqrt[3]{2} + 3 \sqrt[3]{2} + \sqrt{6^{2} \cdot 2}$

Step 1.6

Pull terms out from under the radical.

$5 \sqrt[3]{2} + 3 \sqrt[3]{2} + | 6 | \sqrt{2}$

Step 1.7

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$5 \sqrt[3]{2} + 3 \sqrt[3]{2} + 6 \sqrt{2}$

Step 2

Add $5 \sqrt[3]{2}$ and $3 \sqrt[3]{2}$ .

$8 \sqrt[3]{2} + 6 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt[3]{2} + 6 \sqrt{2}$

Decimal Form:

$18.56464977 \dots$