Algebra Examples

$\sqrt{8 x^{5}} \cdot \sqrt{3 x}$

Step 1

Rewrite $8 x^{5}$ as ${(2 x^{2})}^{2} \cdot (2 x)$ .

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Step 1.1

Factor $4$ out of $8$ .

$\sqrt{4 (2) x^{5}} \cdot \sqrt{3 x}$

Step 1.2

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

$\sqrt{2^{2} \cdot 2 x^{5}} \cdot \sqrt{3 x}$

Step 1.3

Factor out $x^{4}$ .

$\sqrt{2^{2} \cdot 2 (x^{4} x)} \cdot \sqrt{3 x}$

Step 1.4

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Step 1.5

Move $2$ .

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

Step 1.6

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

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

Step 1.7

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $2 x^{2} \sqrt{2 x} \sqrt{3 x}$ .

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Step 3.1

Combine using the product rule for radicals.

$2 x^{2} \sqrt{3 x (2 x)}$

Step 3.2

Multiply $2$ by $3$ .

$2 x^{2} \sqrt{6 x \cdot x}$

Step 3.3

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

$2 x^{2} \sqrt{6 (x^{1} x)}$

Step 3.4

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

$2 x^{2} \sqrt{6 (x^{1} x^{1})}$

Step 3.5

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

$2 x^{2} \sqrt{6 x^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$2 x^{2} \sqrt{6 x^{2}}$

Step 4

Reorder $6$ and $x^{2}$ .

$2 x^{2} \sqrt{x^{2} \cdot 6}$

Step 5

Pull terms out from under the radical.

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

Step 6

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 6.1

Move $x$ .

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

Step 6.2

Multiply $x$ by $x^{2}$ .

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Step 6.2.1

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

$2 (x^{1} x^{2}) \sqrt{6}$

Step 6.2.2

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

$2 x^{1 + 2} \sqrt{6}$

Step 6.3

Add $1$ and $2$ .

$2 x^{3} \sqrt{6}$