Algebra Examples

$\sqrt{3 x^{2}} \cdot 4 \sqrt{10 x^{2}}$

Step 1

Simplify the expression.

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Step 1.1

Rewrite using the commutative property of multiplication.

$4 \sqrt{3 x^{2}} \sqrt{10 x^{2}}$

Step 1.2

Reorder $3$ and $x^{2}$ .

$4 \sqrt{x^{2} \cdot 3} \sqrt{10 x^{2}}$

$4 \sqrt{x^{2} \cdot 3} \sqrt{10 x^{2}}$

Step 2

Pull terms out from under the radical.

$4 (x \sqrt{3}) \sqrt{10 x^{2}}$

Step 3

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

$4 x \sqrt{3} \sqrt{x^{2} \cdot 10}$

Step 4

Pull terms out from under the radical.

$4 x \sqrt{3} (x \sqrt{10})$

Step 5

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

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Step 5.1

Move $x$ .

$4 (x \cdot x) \sqrt{3} \sqrt{10}$

Step 5.2

Multiply $x$ by $x$ .

$4 x^{2} \sqrt{3} \sqrt{10}$

$4 x^{2} \sqrt{3} \sqrt{10}$

Step 6

Multiply $4 x^{2} \sqrt{3} \sqrt{10}$ .

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Step 6.1

Combine using the product rule for radicals.

$4 x^{2} \sqrt{10 \cdot 3}$

Step 6.2

Multiply $10$ by $3$ .

$4 x^{2} \sqrt{30}$

$4 x^{2} \sqrt{30}$

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