Finite Math Examples

$\frac{12 \sqrt{21} - 16}{\sqrt{4}}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{12 \sqrt{21} - 16}{\sqrt{2^{2}}}$

Step 1.2

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

$\frac{12 \sqrt{21} - 16}{2}$

Step 2

Cancel the common factor of $12 \sqrt{21} - 16$ and $2$ .

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Step 2.1

Factor $2$ out of $12 \sqrt{21}$ .

$\frac{2 (6 \sqrt{21}) - 16}{2}$

Step 2.2

Factor $2$ out of $- 16$ .

$\frac{2 (6 \sqrt{21}) + 2 \cdot - 8}{2}$

Step 2.3

Factor $2$ out of $2 (6 \sqrt{21}) + 2 (- 8)$ .

$\frac{2 (6 \sqrt{21} - 8)}{2}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $2$ .

$\frac{2 (6 \sqrt{21} - 8)}{2 (1)}$

Step 2.4.2

Cancel the common factor.

$\frac{2 (6 \sqrt{21} - 8)}{2 \cdot 1}$

Step 2.4.3

Rewrite the expression.

$\frac{6 \sqrt{21} - 8}{1}$

Step 2.4.4

Divide $6 \sqrt{21} - 8$ by $1$ .

$6 \sqrt{21} - 8$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{21} - 8$

Decimal Form:

$19.49545416 \dots$