Precalculus Examples

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

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Apply the distributive property.

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

Step 1.2

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

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

Step 1.3

Combine using the product rule for radicals.

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

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Multiply $3$ by $3$ .

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

Step 2.2

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

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

Step 2.3

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

$2 \sqrt{3} + 3$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3} + 3$

Decimal Form:

$6.46410161 \dots$