Evaluate 5 cube root of 81+ cube root of 375

$5 \sqrt[3]{81} + \sqrt[3]{375}$

Step 1

Simplify each term.

Rewrite $81$ as $3^{3} \cdot 3$ .

Factor $27$ out of $81$ .

$5 \sqrt[3]{27 (3)} + \sqrt[3]{375}$

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

$5 \sqrt[3]{3^{3} \cdot 3} + \sqrt[3]{375}$

$5 \sqrt[3]{3^{3} \cdot 3} + \sqrt[3]{375}$

Pull terms out from under the radical.

$5 (3 \sqrt[3]{3}) + \sqrt[3]{375}$

Multiply $3$ by $5$ .

$15 \sqrt[3]{3} + \sqrt[3]{375}$

Rewrite $375$ as $5^{3} \cdot 3$ .

Factor $125$ out of $375$ .

$15 \sqrt[3]{3} + \sqrt[3]{125 (3)}$

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

$15 \sqrt[3]{3} + \sqrt[3]{5^{3} \cdot 3}$

$15 \sqrt[3]{3} + \sqrt[3]{5^{3} \cdot 3}$

Pull terms out from under the radical.

$15 \sqrt[3]{3} + 5 \sqrt[3]{3}$

$15 \sqrt[3]{3} + 5 \sqrt[3]{3}$

Step 2

Add $15 \sqrt[3]{3}$ and $5 \sqrt[3]{3}$ .

$20 \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$20 \sqrt[3]{3}$

Decimal Form:

$28.84499140 \dots$

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