Calculus Examples

$lim_{x \to c} \sqrt{12 \cdot \frac{3}{4}}$

Step 1

Evaluate the limit of $\sqrt{12 \cdot \frac{3}{4}}$ which is constant as $x$ approaches $c$ .

$\sqrt{12 \cdot \frac{3}{4}}$

Step 2

Simplify the answer.

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Step 2.1

Combine $12$ and $\frac{3}{4}$ .

$\sqrt{\frac{12 \cdot 3}{4}}$

Step 2.2

Reduce the expression by cancelling the common factors.

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Step 2.2.1

Reduce the expression $\frac{12 \cdot 3}{4}$ by cancelling the common factors.

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Step 2.2.1.1

Factor $4$ out of $12 \cdot 3$ .

$\sqrt{\frac{4 (3 \cdot 3)}{4}}$

Step 2.2.1.2

Factor $4$ out of $4$ .

$\sqrt{\frac{4 (3 \cdot 3)}{4 (1)}}$

Step 2.2.1.3

Cancel the common factor.

$\sqrt{\frac{4 (3 \cdot 3)}{4 \cdot 1}}$

Step 2.2.1.4

Rewrite the expression.

$\sqrt{\frac{3 \cdot 3}{1}}$

Step 2.2.2

Divide $3 \cdot 3$ by $1$ .

$\sqrt{3 \cdot 3}$

Step 2.3

Multiply $3$ by $3$ .

$\sqrt{9}$

Step 2.4

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2}}$

Step 2.5

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

$3$