Algebra Examples

$3 \sqrt{7} \cdot 7 \sqrt{14}$

Step 1

Multiply $7$ by $3$ .

$21 \sqrt{7} \sqrt{14}$

Step 2

Multiply $21 \sqrt{7} \sqrt{14}$ .

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Step 2.1

Combine using the product rule for radicals.

$21 \sqrt{14 \cdot 7}$

Step 2.2

Multiply $14$ by $7$ .

$21 \sqrt{98}$

Step 3

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 3.1

Factor $49$ out of $98$ .

$21 \sqrt{49 (2)}$

Step 3.2

Rewrite $49$ as $7^{2}$ .

$21 \sqrt{7^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$21 (| 7 | \sqrt{2})$

Step 5

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$21 (7 \sqrt{2})$

Step 6

Multiply $7$ by $21$ .

$147 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$147 \sqrt{2}$

Decimal Form:

$207.88939366 \dots$