Basic Math Examples

\sqrt{5} \times \sqrt{10}

$\sqrt{5} \times \sqrt{10}$

Step 1

Combine using the product rule for radicals.

\sqrt{5 \cdot 10}

$\sqrt{5 \cdot 10}$

Step 2

Multiply

5

$5$ by

10

$10$ .

\sqrt{50}

$\sqrt{50}$

Step 3

Rewrite

50

$50$ as

5^{2} \cdot 2

$5^{2} \cdot 2$ .

Tap for more steps...

Step 3.1

Factor

25

$25$ out of

50

$50$ .

\sqrt{25 (2)}

$\sqrt{25 (2)}$

Step 3.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

\sqrt{5^{2} \cdot 2}

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

\sqrt{5^{2} \cdot 2}

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

Step 4

Pull terms out from under the radical.

5 \sqrt{2}

$5 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

5 \sqrt{2}

$5 \sqrt{2}$

Decimal Form:

7.07106781 \dots

$7.07106781 \dots$

$\sqrt[]{5} \times \sqrt[]{10}$

(

(

)

)

|

|

[

[

]

]

√

√





≥

≥













π

π





7

7

8

8

9

9













≤

≤





















4

4

5

5

6

6

/

/

^

^

×

×

>

>













!

!





1

1

2

2

3

3

-

-

+

+

÷

÷

<

<



















,

,

0

0

.

.

%

%



=

=









⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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