Algebra Examples

$\sqrt{5 x^{2}} \cdot \sqrt{12 x^{3}}$

Step 1

Reorder $5$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 5} \cdot \sqrt{12 x^{3}}$

Step 2

Pull terms out from under the radical.

$x \sqrt{5} \cdot \sqrt{12 x^{3}}$

Step 3

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

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Step 3.1

Factor $4$ out of $12$ .

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

Step 3.2

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

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

Step 3.3

Factor out $x^{2}$ .

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

Step 3.4

Move $3$ .

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

Step 3.5

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

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

Step 3.6

Add parentheses.

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $x$ by $x$ by adding the exponents.

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Step 5.1

Move $x$ .

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

Step 5.2

Multiply $x$ by $x$ .

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

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

Step 6

Multiply $x^{2} \sqrt{5} (2 \sqrt{3 x})$ .

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Step 6.1

Combine using the product rule for radicals.

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

Step 6.2

Multiply $5$ by $3$ .

$x^{2} (2 \sqrt{15 x})$

$x^{2} (2 \sqrt{15 x})$

Step 7

Rewrite using the commutative property of multiplication.

$2 x^{2} \sqrt{15 x}$

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