Algebra Examples

$2 \sqrt{7 x} \cdot 3 \sqrt{14 x^{2}}$

Step 1

Reorder $14$ and $x^{2}$ .

$2 \sqrt{7 x} \cdot (3 \sqrt{x^{2} \cdot 14})$

Step 2

Pull terms out from under the radical.

$2 \sqrt{7 x} \cdot (3 (x \sqrt{14}))$

Step 3

Multiply $2 \sqrt{7 x} (3 x \sqrt{14})$ .

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Step 3.1

Multiply $3$ by $2$ .

$6 \sqrt{7 x} (x \sqrt{14})$

Step 3.2

Combine using the product rule for radicals.

$6 (x \sqrt{7 x \cdot 14})$

Step 3.3

Multiply $14$ by $7$ .

$6 (x \sqrt{98 x})$

$6 (x \sqrt{98 x})$

Step 4

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

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Step 4.1

Factor $49$ out of $98$ .

$6 (x \sqrt{49 (2) x})$

Step 4.2

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

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

Step 4.3

Add parentheses.

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Simplify the expression.

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Step 6.1

Rewrite using the commutative property of multiplication.

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

Step 6.2

Multiply $7$ by $6$ .

$42 x \sqrt{2 x}$

$42 x \sqrt{2 x}$

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