Basic Math Examples

$3 a \sqrt{2} \cdot (7 a \sqrt{10})$

Step 1

Multiply $a$ by $a$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $a$ .

$3 (a \cdot a) \sqrt{2} \cdot (7 \sqrt{10})$

Step 1.2

Multiply $a$ by $a$ .

$3 a^{2} \sqrt{2} \cdot (7 \sqrt{10})$

$3 a^{2} \sqrt{2} \cdot (7 \sqrt{10})$

Step 2

Multiply $3 a^{2} \sqrt{2} (7 \sqrt{10})$ .

Tap for more steps...

Step 2.1

Multiply $7$ by $3$ .

$21 a^{2} \sqrt{2} \sqrt{10}$

Step 2.2

Combine using the product rule for radicals.

$21 a^{2} \sqrt{10 \cdot 2}$

Step 2.3

Multiply $10$ by $2$ .

$21 a^{2} \sqrt{20}$

$21 a^{2} \sqrt{20}$

Step 3

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

Tap for more steps...

Step 3.1

Factor $4$ out of $20$ .

$21 a^{2} \sqrt{4 (5)}$

Step 3.2

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

$21 a^{2} \sqrt{2^{2} \cdot 5}$

$21 a^{2} \sqrt{2^{2} \cdot 5}$

Step 4

Pull terms out from under the radical.

$21 a^{2} (2 \sqrt{5})$

Step 5

Multiply $2$ by $21$ .

$42 a^{2} \sqrt{5}$

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