Basic Math Examples

$\sqrt{21} \cdot \sqrt{10 w^{4}}$

Step 1

Rewrite $10 w^{4}$ as ${(w^{2})}^{2} \cdot 10$ .

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Step 1.1

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

$\sqrt{21} \cdot \sqrt{10 {(w^{2})}^{2}}$

Step 1.2

Reorder $10$ and ${(w^{2})}^{2}$ .

$\sqrt{21} \cdot \sqrt{{(w^{2})}^{2} \cdot 10}$

$\sqrt{21} \cdot \sqrt{{(w^{2})}^{2} \cdot 10}$

Step 2

Pull terms out from under the radical.

$\sqrt{21} \cdot (w^{2} \sqrt{10})$

Step 3

Multiply $\sqrt{21} (w^{2} \sqrt{10})$ .

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Step 3.1

Combine using the product rule for radicals.

$w^{2} \sqrt{21 \cdot 10}$

Step 3.2

Multiply $21$ by $10$ .

$w^{2} \sqrt{210}$

$w^{2} \sqrt{210}$

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