Algebra Examples

$\sqrt{6} (5 + \sqrt{3})$

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Apply the distributive property.

$\sqrt{6} \cdot 5 + \sqrt{6} \sqrt{3}$

Step 1.2

Move $5$ to the left of $\sqrt{6}$ .

$5 \cdot \sqrt{6} + \sqrt{6} \sqrt{3}$

Step 1.3

Combine using the product rule for radicals.

$5 \cdot \sqrt{6} + \sqrt{6 \cdot 3}$

$5 \cdot \sqrt{6} + \sqrt{6 \cdot 3}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Multiply $6$ by $3$ .

$5 \sqrt{6} + \sqrt{18}$

Step 2.2

Rewrite $18$ as $3^{2} \cdot 2$ .

Tap for more steps...

Step 2.2.1

Factor $9$ out of $18$ .

$5 \sqrt{6} + \sqrt{9 (2)}$

Step 2.2.2

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

$5 \sqrt{6} + \sqrt{3^{2} \cdot 2}$

$5 \sqrt{6} + \sqrt{3^{2} \cdot 2}$

Step 2.3

Pull terms out from under the radical.

$5 \sqrt{6} + 3 \sqrt{2}$

$5 \sqrt{6} + 3 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{6} + 3 \sqrt{2}$

Decimal Form:

$16.49008940 \dots$

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