Basic Math Examples

$4 \sqrt{48} \cdot \sqrt{20}$

Step 1

Rewrite

$48$ as

$4^{2} \cdot 3$ .

Tap for more steps...

Step 1.1

Factor

$16$ out of

$48$ .

$4 \sqrt{16 (3)} \cdot \sqrt{20}$

Step 1.2

Rewrite

$16$ as

$4^{2}$ .

$4 \sqrt{4^{2} \cdot 3} \cdot \sqrt{20}$

$4 \sqrt{4^{2} \cdot 3} \cdot \sqrt{20}$

Step 2

Pull terms out from under the radical.

$4 (4 \sqrt{3}) \cdot \sqrt{20}$

Step 3

Multiply

$4$ by

$4$ .

$16 \sqrt{3} \cdot \sqrt{20}$

Step 4

Rewrite

$20$ as

$2^{2} \cdot 5$ .

Tap for more steps...

Step 4.1

Factor

$4$ out of

$20$ .

$16 \sqrt{3} \cdot \sqrt{4 (5)}$

Step 4.2

Rewrite

$4$ as

$2^{2}$ .

$16 \sqrt{3} \cdot \sqrt{2^{2} \cdot 5}$

$16 \sqrt{3} \cdot \sqrt{2^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$16 \sqrt{3} \cdot (2 \sqrt{5})$

Step 6

Multiply

$16 \sqrt{3} (2 \sqrt{5})$ .

Tap for more steps...

Step 6.1

Multiply

$2$ by

$16$ .

$32 \sqrt{3} \sqrt{5}$

Step 6.2

Combine using the product rule for radicals.

$32 \sqrt{5 \cdot 3}$

Step 6.3

Multiply

$5$ by

$3$ .

$32 \sqrt{15}$

$32 \sqrt{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$32 \sqrt{15}$

Decimal Form:

$123.93546707 \dots$

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