Algebra Examples

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

Step 1

Multiply $3$ by $7$ .

$2 \sqrt{21 x \sqrt{14 x^{2}}}$

Step 2

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

$2 \sqrt{21 x \sqrt{x^{2} \cdot 14}}$

Step 3

Pull terms out from under the radical.

$2 \sqrt{21 x \cdot x \sqrt{14}}$

Step 4

Combine exponents.

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Step 4.1

Raise $x$ to the power of $1$ .

$2 \sqrt{21 (x^{1} x) \sqrt{14}}$

Step 4.2

Raise $x$ to the power of $1$ .

$2 \sqrt{21 (x^{1} x^{1}) \sqrt{14}}$

Step 4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \sqrt{21 x^{1 + 1} \sqrt{14}}$

Step 4.4

Add $1$ and $1$ .

$2 \sqrt{21 x^{2} \sqrt{14}}$

Step 5

Rewrite $21 x^{2} \sqrt{14}$ as $x^{2} \cdot (21 \sqrt{14})$ .

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Step 5.1

Reorder $21$ and $x^{2}$ .

$2 \sqrt{x^{2} \cdot 21 \sqrt{14}}$

Step 5.2

Add parentheses.

$2 \sqrt{x^{2} \cdot (21 \sqrt{14})}$

Step 6

Pull terms out from under the radical.

$2 x \sqrt{21 \sqrt{14}}$