Algebra Examples

$\sqrt{3} (\sqrt{3} + 2)$

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

$\sqrt{3} \sqrt{3} + \sqrt{3} \cdot 2$

Step 1.2

Combine using the product rule for radicals.

$\sqrt{3 \cdot 3} + \sqrt{3} \cdot 2$

Step 1.3

Move $2$ to the left of $\sqrt{3}$ .

$\sqrt{3 \cdot 3} + 2 \cdot \sqrt{3}$

Step 2

Simplify each term.

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Step 2.1

Multiply $3$ by $3$ .

$\sqrt{9} + 2 \cdot \sqrt{3}$

Step 2.2

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

$\sqrt{3^{2}} + 2 \cdot \sqrt{3}$

Step 2.3

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

$3 + 2 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 + 2 \sqrt{3}$

Decimal Form:

$6.46410161 \dots$