Algebra Examples

$\sqrt{6} \cdot 7 \sqrt{18}$

Step 1

Move $7$ to the left of $\sqrt{6}$ .

$7 \cdot \sqrt{6} \sqrt{18}$

Step 2

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

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Step 2.1

Factor $9$ out of $18$ .

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

Step 2.2

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

$7 \sqrt{6} \sqrt{3^{2} \cdot 2}$

Step 3

Pull terms out from under the radical.

$7 \sqrt{6} (| 3 | \sqrt{2})$

Step 4

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$7 \sqrt{6} (3 \sqrt{2})$

Step 5

Multiply $7 \sqrt{6} (3 \sqrt{2})$ .

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Step 5.1

Multiply $3$ by $7$ .

$21 \sqrt{6} \sqrt{2}$

Step 5.2

Combine using the product rule for radicals.

$21 \sqrt{2 \cdot 6}$

Step 5.3

Multiply $2$ by $6$ .

$21 \sqrt{12}$

Step 6

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

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Step 6.1

Factor $4$ out of $12$ .

$21 \sqrt{4 (3)}$

Step 6.2

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

$21 \sqrt{2^{2} \cdot 3}$

Step 7

Pull terms out from under the radical.

$21 (| 2 | \sqrt{3})$

Step 8

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$21 (2 \sqrt{3})$

Step 9

Multiply $2$ by $21$ .

$42 \sqrt{3}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$42 \sqrt{3}$

Decimal Form:

$72.74613391 \dots$