Basic Math Examples

$\frac{45}{23} + 23 + 4 \sqrt{12}$

Step 1

Find the common denominator.

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Step 1.1

Write $23$ as a fraction with denominator $1$ .

$\frac{45}{23} + \frac{23}{1} + 4 \sqrt{12}$

Step 1.2

Multiply $\frac{23}{1}$ by $\frac{23}{23}$ .

$\frac{45}{23} + \frac{23}{1} \cdot \frac{23}{23} + 4 \sqrt{12}$

Step 1.3

Multiply $\frac{23}{1}$ by $\frac{23}{23}$ .

$\frac{45}{23} + \frac{23 \cdot 23}{23} + 4 \sqrt{12}$

Step 1.4

Write $4 \sqrt{12}$ as a fraction with denominator $1$ .

$\frac{45}{23} + \frac{23 \cdot 23}{23} + \frac{4 \sqrt{12}}{1}$

Step 1.5

Multiply $\frac{4 \sqrt{12}}{1}$ by $\frac{23}{23}$ .

$\frac{45}{23} + \frac{23 \cdot 23}{23} + \frac{4 \sqrt{12}}{1} \cdot \frac{23}{23}$

Step 1.6

Multiply $\frac{4 \sqrt{12}}{1}$ by $\frac{23}{23}$ .

$\frac{45}{23} + \frac{23 \cdot 23}{23} + \frac{4 \sqrt{12} \cdot 23}{23}$

Step 2

Combine the numerators over the common denominator.

$\frac{45 + 23 \cdot 23 + 4 \sqrt{12} \cdot 23}{23}$

Step 3

Simplify each term.

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Step 3.1

Multiply $23$ by $23$ .

$\frac{45 + 529 + 4 \sqrt{12} \cdot 23}{23}$

Step 3.2

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 3.2.1

Factor $4$ out of $12$ .

$\frac{45 + 529 + 4 \sqrt{4 (3)} \cdot 23}{23}$

Step 3.2.2

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

$\frac{45 + 529 + 4 \sqrt{2^{2} \cdot 3} \cdot 23}{23}$

Step 3.3

Pull terms out from under the radical.

$\frac{45 + 529 + 4 (2 \sqrt{3}) \cdot 23}{23}$

Step 3.4

Multiply $2$ by $4$ .

$\frac{45 + 529 + 8 \sqrt{3} \cdot 23}{23}$

Step 3.5

Multiply $23$ by $8$ .

$\frac{45 + 529 + 184 \sqrt{3}}{23}$

Step 4

Add $45$ and $529$ .

$\frac{574 + 184 \sqrt{3}}{23}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{574 + 184 \sqrt{3}}{23}$

Decimal Form:

$38.81292819 \dots$