Basic Math Examples

$2^{3} + \sqrt{25} \cdot 3 - 4^{2} \div \sqrt{4}$

Step 1

Find the common denominator.

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Step 1.1

Write $2^{3}$ as a fraction with denominator $1$ .

$\frac{2^{3}}{1} + \sqrt{25} \cdot 3 - 4^{2} \div \sqrt{4}$

Step 1.2

Multiply $\frac{2^{3}}{1}$ by $\frac{\sqrt{4}}{\sqrt{4}}$ .

$\frac{2^{3}}{1} \cdot \frac{\sqrt{4}}{\sqrt{4}} + \sqrt{25} \cdot 3 - 4^{2} \div \sqrt{4}$

Step 1.3

Multiply $\frac{2^{3}}{1}$ by $\frac{\sqrt{4}}{\sqrt{4}}$ .

$\frac{2^{3} \sqrt{4}}{\sqrt{4}} + \sqrt{25} \cdot 3 - 4^{2} \div \sqrt{4}$

Step 1.4

Write $\sqrt{25} \cdot 3$ as a fraction with denominator $1$ .

$\frac{2^{3} \sqrt{4}}{\sqrt{4}} + \frac{\sqrt{25} \cdot 3}{1} - 4^{2} \div \sqrt{4}$

Step 1.5

Multiply $\frac{\sqrt{25} \cdot 3}{1}$ by $\frac{\sqrt{4}}{\sqrt{4}}$ .

$\frac{2^{3} \sqrt{4}}{\sqrt{4}} + \frac{\sqrt{25} \cdot 3}{1} \cdot \frac{\sqrt{4}}{\sqrt{4}} - 4^{2} \div \sqrt{4}$

Step 1.6

Multiply $\frac{\sqrt{25} \cdot 3}{1}$ by $\frac{\sqrt{4}}{\sqrt{4}}$ .

$\frac{2^{3} \sqrt{4}}{\sqrt{4}} + \frac{\sqrt{25} \cdot 3 \sqrt{4}}{\sqrt{4}} - 4^{2} \div \sqrt{4}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{2^{3} \sqrt{4} + \sqrt{25} \cdot 3 \sqrt{4} - 4^{2}}{\sqrt{4}}$

Step 2.2

Simplify each term.

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Step 2.2.1

Raise $2$ to the power of $3$ .

$\frac{8 \sqrt{4} + \sqrt{25} \cdot 3 \sqrt{4} - 4^{2}}{\sqrt{4}}$

Step 2.2.2

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

$\frac{8 \sqrt{2^{2}} + \sqrt{25} \cdot 3 \sqrt{4} - 4^{2}}{\sqrt{4}}$

Step 2.2.3

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

$\frac{8 \cdot 2 + \sqrt{25} \cdot 3 \sqrt{4} - 4^{2}}{\sqrt{4}}$

Step 2.2.4

Multiply $8$ by $2$ .

$\frac{16 + \sqrt{25} \cdot 3 \sqrt{4} - 4^{2}}{\sqrt{4}}$

Step 2.2.5

Rewrite $25$ as $5^{2}$ .

$\frac{16 + \sqrt{5^{2}} \cdot 3 \sqrt{4} - 4^{2}}{\sqrt{4}}$

Step 2.2.6

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

$\frac{16 + 5 \cdot 3 \sqrt{4} - 4^{2}}{\sqrt{4}}$

Step 2.2.7

Multiply $5$ by $3$ .

$\frac{16 + 15 \sqrt{4} - 4^{2}}{\sqrt{4}}$

Step 2.2.8

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

$\frac{16 + 15 \sqrt{2^{2}} - 4^{2}}{\sqrt{4}}$

Step 2.2.9

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

$\frac{16 + 15 \cdot 2 - 4^{2}}{\sqrt{4}}$

Step 2.2.10

Multiply $15$ by $2$ .

$\frac{16 + 30 - 4^{2}}{\sqrt{4}}$

Step 2.2.11

Raise $4$ to the power of $2$ .

$\frac{16 + 30 - 1 \cdot 16}{\sqrt{4}}$

Step 2.2.12

Multiply $- 1$ by $16$ .

$\frac{16 + 30 - 16}{\sqrt{4}}$

Step 2.3

Simplify by adding and subtracting.

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Step 2.3.1

Add $16$ and $30$ .

$\frac{46 - 16}{\sqrt{4}}$

Step 2.3.2

Subtract $16$ from $46$ .

$\frac{30}{\sqrt{4}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{30}{\sqrt{2^{2}}}$

Step 3.2

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

$\frac{30}{2}$

Step 4

Divide $30$ by $2$ .

$15$