Algebra Examples

$\sqrt{6 x^{2}} \cdot \sqrt{48 x}$

Step 1

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

$\sqrt{x^{2} \cdot 6} \cdot \sqrt{48 x}$

Step 2

Pull terms out from under the radical.

$x \sqrt{6} \cdot \sqrt{48 x}$

Step 3

Rewrite $48 x$ as ${(2^{2})}^{2} \cdot (3 x)$ .

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Step 3.1

Factor $16$ out of $48$ .

$x \sqrt{6} \cdot \sqrt{16 (3) x}$

Step 3.2

Rewrite $16$ as $4^{2}$ .

$x \sqrt{6} \cdot \sqrt{4^{2} \cdot 3 x}$

Step 3.3

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

$x \sqrt{6} \cdot \sqrt{{(2^{2})}^{2} \cdot 3 x}$

Step 3.4

Add parentheses.

$x \sqrt{6} \cdot \sqrt{{(2^{2})}^{2} \cdot (3 x)}$

$x \sqrt{6} \cdot \sqrt{{(2^{2})}^{2} \cdot (3 x)}$

Step 4

Pull terms out from under the radical.

$x \sqrt{6} \cdot (2^{2} \sqrt{3 x})$

Step 5

Raise $2$ to the power of $2$ .

$x \sqrt{6} \cdot (4 \sqrt{3 x})$

Step 6

Multiply $x \sqrt{6} (4 \sqrt{3 x})$ .

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Step 6.1

Combine using the product rule for radicals.

$x (4 \sqrt{6 (3 x)})$

Step 6.2

Multiply $6$ by $3$ .

$x (4 \sqrt{18 x})$

$x (4 \sqrt{18 x})$

Step 7

Rewrite using the commutative property of multiplication.

$4 x \sqrt{18 x}$

Step 8

Rewrite $18 x$ as $3^{2} \cdot (2 x)$ .

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Step 8.1

Factor $9$ out of $18$ .

$4 x \sqrt{9 (2) x}$

Step 8.2

Rewrite $9$ as $3^{2}$ .

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

Step 8.3

Add parentheses.

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

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

Step 9

Pull terms out from under the radical.

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

Step 10

Multiply $3$ by $4$ .

$12 x \sqrt{2 x}$

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