Precalculus Examples

$2 \sqrt{18} + 9 \sqrt{7} - \sqrt{63}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 1.1.1

Factor $9$ out of $18$ .

$2 \sqrt{9 (2)} + 9 \sqrt{7} - \sqrt{63}$

Step 1.1.2

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

$2 \sqrt{3^{2} \cdot 2} + 9 \sqrt{7} - \sqrt{63}$

$2 \sqrt{3^{2} \cdot 2} + 9 \sqrt{7} - \sqrt{63}$

Step 1.2

Pull terms out from under the radical.

$2 (3 \sqrt{2}) + 9 \sqrt{7} - \sqrt{63}$

Step 1.3

Multiply $3$ by $2$ .

$6 \sqrt{2} + 9 \sqrt{7} - \sqrt{63}$

Step 1.4

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

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Step 1.4.1

Factor $9$ out of $63$ .

$6 \sqrt{2} + 9 \sqrt{7} - \sqrt{9 (7)}$

Step 1.4.2

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

$6 \sqrt{2} + 9 \sqrt{7} - \sqrt{3^{2} \cdot 7}$

$6 \sqrt{2} + 9 \sqrt{7} - \sqrt{3^{2} \cdot 7}$

Step 1.5

Pull terms out from under the radical.

$6 \sqrt{2} + 9 \sqrt{7} - (3 \sqrt{7})$

Step 1.6

Multiply $3$ by $- 1$ .

$6 \sqrt{2} + 9 \sqrt{7} - 3 \sqrt{7}$

$6 \sqrt{2} + 9 \sqrt{7} - 3 \sqrt{7}$

Step 2

Subtract $3 \sqrt{7}$ from $9 \sqrt{7}$ .

$6 \sqrt{2} + 6 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{2} + 6 \sqrt{7}$

Decimal Form:

$24.35978924 \dots$

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