Basic Math Examples

$4^{3} \sqrt{40} + \sqrt[3]{625}$

Step 1

Raise $4$ to the power of $3$ .

$64 \sqrt{40} + \sqrt[3]{625}$

Step 2

Rewrite $40$ as $2^{2} \cdot 10$ .

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Step 2.1

Factor $4$ out of $40$ .

$64 \sqrt{4 (10)} + \sqrt[3]{625}$

Step 2.2

Rewrite $4$ as $2^{2}$ .

$64 \sqrt{2^{2} \cdot 10} + \sqrt[3]{625}$

$64 \sqrt{2^{2} \cdot 10} + \sqrt[3]{625}$

Step 3

Pull terms out from under the radical.

$64 (2 \sqrt{10}) + \sqrt[3]{625}$

Step 4

Multiply $2$ by $64$ .

$128 \sqrt{10} + \sqrt[3]{625}$

Step 5

Rewrite $625$ as $5^{3} \cdot 5$ .

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Step 5.1

Factor $125$ out of $625$ .

$128 \sqrt{10} + \sqrt[3]{125 (5)}$

Step 5.2

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

$128 \sqrt{10} + \sqrt[3]{5^{3} \cdot 5}$

$128 \sqrt{10} + \sqrt[3]{5^{3} \cdot 5}$

Step 6

Pull terms out from under the radical.

$128 \sqrt{10} + 5 \sqrt[3]{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$128 \sqrt{10} + 5 \sqrt[3]{5}$

Decimal Form:

$413.32142023 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$