Basic Math Examples

$\sqrt{3} (\sqrt{3} + 4 \sqrt{14})$

Step 1

Apply the distributive property.

$\sqrt{3} \sqrt{3} + \sqrt{3} (4 \sqrt{14})$

Step 2

Combine using the product rule for radicals.

$\sqrt{3 \cdot 3} + \sqrt{3} (4 \sqrt{14})$

Step 3

Multiply $\sqrt{3} (4 \sqrt{14})$ .

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Step 3.1

Combine using the product rule for radicals.

$\sqrt{3 \cdot 3} + 4 \sqrt{3 \cdot 14}$

Step 3.2

Multiply $3$ by $14$ .

$\sqrt{3 \cdot 3} + 4 \sqrt{42}$

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $3$ .

$\sqrt{9} + 4 \sqrt{42}$

Step 4.2

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

$\sqrt{3^{2}} + 4 \sqrt{42}$

Step 4.3

Pull terms out from under the radical, assuming positive real numbers.

$3 + 4 \sqrt{42}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$3 + 4 \sqrt{42}$

Decimal Form:

$28.92296279 \dots$