Algebra Examples

$\sqrt{10 x^{2}} \cdot \sqrt{5 x}$

Step 1

Reorder $10$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 10} \cdot \sqrt{5 x}$

Step 2

Pull terms out from under the radical.

$x \sqrt{10} \cdot \sqrt{5 x}$

Step 3

Multiply $x \sqrt{10} \sqrt{5 x}$ .

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Step 3.1

Combine using the product rule for radicals.

$x \sqrt{5 x \cdot 10}$

Step 3.2

Multiply $10$ by $5$ .

$x \sqrt{50 x}$

$x \sqrt{50 x}$

Step 4

Rewrite $50 x$ as $5^{2} \cdot (2 x)$ .

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Step 4.1

Factor $25$ out of $50$ .

$x \sqrt{25 (2) x}$

Step 4.2

Rewrite $25$ as $5^{2}$ .

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

Step 4.3

Add parentheses.

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Rewrite using the commutative property of multiplication.

$5 x \sqrt{2 x}$

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