Pre-Algebra Examples

$5 \sqrt{10} (\sqrt{2} + 3)$

Step 1

Apply the distributive property.

$5 \sqrt{10} \sqrt{2} + 5 \sqrt{10} \cdot 3$

Step 2

Multiply $5 \sqrt{10} \sqrt{2}$ .

Tap for more steps...

Step 2.1

Combine using the product rule for radicals.

$5 \sqrt{2 \cdot 10} + 5 \sqrt{10} \cdot 3$

Step 2.2

Multiply $2$ by $10$ .

$5 \sqrt{20} + 5 \sqrt{10} \cdot 3$

$5 \sqrt{20} + 5 \sqrt{10} \cdot 3$

Step 3

Multiply $3$ by $5$ .

$5 \sqrt{20} + 15 \sqrt{10}$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Rewrite $20$ as $2^{2} \cdot 5$ .

Tap for more steps...

Step 4.1.1

Factor $4$ out of $20$ .

$5 \sqrt{4 (5)} + 15 \sqrt{10}$

Step 4.1.2

Rewrite $4$ as $2^{2}$ .

$5 \sqrt{2^{2} \cdot 5} + 15 \sqrt{10}$

$5 \sqrt{2^{2} \cdot 5} + 15 \sqrt{10}$

Step 4.2

Pull terms out from under the radical.

$5 (2 \sqrt{5}) + 15 \sqrt{10}$

Step 4.3

Multiply $2$ by $5$ .

$10 \sqrt{5} + 15 \sqrt{10}$

$10 \sqrt{5} + 15 \sqrt{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{5} + 15 \sqrt{10}$

Decimal Form:

$69.79484467 \dots$

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