Basic Math Examples

$(2 \sqrt{5 + 3}) (\sqrt{5} - 1)$

Step 1

Add $5$ and $3$ .

$2 \sqrt{8} (\sqrt{5} - 1)$

Step 2

Rewrite $8$ as $2^{2} \cdot 2$ .

Tap for more steps...

Step 2.1

Factor $4$ out of $8$ .

$2 \sqrt{4 (2)} (\sqrt{5} - 1)$

Step 2.2

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

$2 \sqrt{2^{2} \cdot 2} (\sqrt{5} - 1)$

$2 \sqrt{2^{2} \cdot 2} (\sqrt{5} - 1)$

Step 3

Pull terms out from under the radical.

$2 (2 \sqrt{2}) (\sqrt{5} - 1)$

Step 4

Multiply $2$ by $2$ .

$4 \sqrt{2} (\sqrt{5} - 1)$

Step 5

Apply the distributive property.

$4 \sqrt{2} \sqrt{5} + 4 \sqrt{2} \cdot - 1$

Step 6

Multiply $4 \sqrt{2} \sqrt{5}$ .

Tap for more steps...

Step 6.1

Combine using the product rule for radicals.

$4 \sqrt{5 \cdot 2} + 4 \sqrt{2} \cdot - 1$

Step 6.2

Multiply $5$ by $2$ .

$4 \sqrt{10} + 4 \sqrt{2} \cdot - 1$

$4 \sqrt{10} + 4 \sqrt{2} \cdot - 1$

Step 7

Multiply $- 1$ by $4$ .

$4 \sqrt{10} - 4 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{10} - 4 \sqrt{2}$

Decimal Form:

$6.99225639 \dots$

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