Algebra Examples

$\sqrt{6 a} \cdot 2 \sqrt{2 a b}$

Step 1

Rewrite using the commutative property of multiplication.

$2 \sqrt{6 a} \sqrt{2 a b}$

Step 2

Multiply $2 \sqrt{6 a} \sqrt{2 a b}$ .

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Step 2.1

Combine using the product rule for radicals.

$2 \sqrt{2 a b (6 a)}$

Step 2.2

Multiply $6$ by $2$ .

$2 \sqrt{12 a b a}$

Step 2.3

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

$2 \sqrt{12 (a^{1} a) b}$

Step 2.4

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

$2 \sqrt{12 (a^{1} a^{1}) b}$

Step 2.5

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

$2 \sqrt{12 a^{1 + 1} b}$

Step 2.6

Add $1$ and $1$ .

$2 \sqrt{12 a^{2} b}$

Step 3

Rewrite $12 a^{2} b$ as ${(2 a)}^{2} \cdot (3 b)$ .

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Step 3.1

Factor $4$ out of $12$ .

$2 \sqrt{4 (3) a^{2} b}$

Step 3.2

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

$2 \sqrt{2^{2} \cdot 3 a^{2} b}$

Step 3.3

Move $3$ .

$2 \sqrt{2^{2} a^{2} \cdot 3 b}$

Step 3.4

Rewrite $2^{2} a^{2}$ as ${(2 a)}^{2}$ .

$2 \sqrt{{(2 a)}^{2} \cdot 3 b}$

Step 3.5

Add parentheses.

$2 \sqrt{{(2 a)}^{2} \cdot (3 b)}$

Step 4

Pull terms out from under the radical.

$2 (2 a \sqrt{3 b})$

Step 5

Multiply $2$ by $2$ .

$4 a \sqrt{3 b}$