Algebra Examples

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

Step 1

Move $7$ to the left of $\sqrt{3}$ .

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

Step 2

Multiply $7 \sqrt{3} \sqrt{6}$ .

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Step 2.1

Combine using the product rule for radicals.

$7 \sqrt{6 \cdot 3}$

Step 2.2

Multiply $6$ by $3$ .

$7 \sqrt{18}$

Step 3

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

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Step 3.1

Factor $9$ out of $18$ .

$7 \sqrt{9 (2)}$

Step 3.2

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

$7 (3 \sqrt{2})$

Step 6

Multiply $3$ by $7$ .

$21 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$21 \sqrt{2}$

Decimal Form:

$29.69848480 \dots$