Precalculus Examples

$3 \sqrt{28 x} - 4 \sqrt{63 x}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $28 x$ as $2^{2} \cdot (7 x)$ .

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Step 1.1.1

Factor $4$ out of $28$ .

$3 \sqrt{4 (7) x} - 4 \sqrt{63 x}$

Step 1.1.2

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

$3 \sqrt{2^{2} \cdot 7 x} - 4 \sqrt{63 x}$

Step 1.1.3

Add parentheses.

$3 \sqrt{2^{2} \cdot (7 x)} - 4 \sqrt{63 x}$

$3 \sqrt{2^{2} \cdot (7 x)} - 4 \sqrt{63 x}$

Step 1.2

Pull terms out from under the radical.

$3 (2 \sqrt{7 x}) - 4 \sqrt{63 x}$

Step 1.3

Multiply $2$ by $3$ .

$6 \sqrt{7 x} - 4 \sqrt{63 x}$

Step 1.4

Rewrite $63 x$ as $3^{2} \cdot (7 x)$ .

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Step 1.4.1

Factor $9$ out of $63$ .

$6 \sqrt{7 x} - 4 \sqrt{9 (7) x}$

Step 1.4.2

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

$6 \sqrt{7 x} - 4 \sqrt{3^{2} \cdot 7 x}$

Step 1.4.3

Add parentheses.

$6 \sqrt{7 x} - 4 \sqrt{3^{2} \cdot (7 x)}$

$6 \sqrt{7 x} - 4 \sqrt{3^{2} \cdot (7 x)}$

Step 1.5

Pull terms out from under the radical.

$6 \sqrt{7 x} - 4 (3 \sqrt{7 x})$

Step 1.6

Multiply $3$ by $- 4$ .

$6 \sqrt{7 x} - 12 \sqrt{7 x}$

$6 \sqrt{7 x} - 12 \sqrt{7 x}$

Step 2

Subtract $12 \sqrt{7 x}$ from $6 \sqrt{7 x}$ .

$- 6 \sqrt{7 x}$

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