Basic Math Examples

$\sqrt{50} + \sqrt{72} + 2 \sqrt{8} + \sqrt{32}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $50$ as $5^{2} \cdot 2$ .

Tap for more steps...

Step 1.1.1

Factor $25$ out of $50$ .

$\sqrt{25 (2)} + \sqrt{72} + 2 \sqrt{8} + \sqrt{32}$

Step 1.1.2

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2} + \sqrt{72} + 2 \sqrt{8} + \sqrt{32}$

Step 1.2

Pull terms out from under the radical.

$5 \sqrt{2} + \sqrt{72} + 2 \sqrt{8} + \sqrt{32}$

Step 1.3

Rewrite $72$ as $6^{2} \cdot 2$ .

Tap for more steps...

Step 1.3.1

Factor $36$ out of $72$ .

$5 \sqrt{2} + \sqrt{36 (2)} + 2 \sqrt{8} + \sqrt{32}$

Step 1.3.2

Rewrite $36$ as $6^{2}$ .

$5 \sqrt{2} + \sqrt{6^{2} \cdot 2} + 2 \sqrt{8} + \sqrt{32}$

Step 1.4

Pull terms out from under the radical.

$5 \sqrt{2} + 6 \sqrt{2} + 2 \sqrt{8} + \sqrt{32}$

Step 1.5

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

Tap for more steps...

Step 1.5.1

Factor $4$ out of $8$ .

$5 \sqrt{2} + 6 \sqrt{2} + 2 \sqrt{4 (2)} + \sqrt{32}$

Step 1.5.2

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

$5 \sqrt{2} + 6 \sqrt{2} + 2 \sqrt{2^{2} \cdot 2} + \sqrt{32}$

Step 1.6

Pull terms out from under the radical.

$5 \sqrt{2} + 6 \sqrt{2} + 2 (2 \sqrt{2}) + \sqrt{32}$

Step 1.7

Multiply $2$ by $2$ .

$5 \sqrt{2} + 6 \sqrt{2} + 4 \sqrt{2} + \sqrt{32}$

Step 1.8

Rewrite $32$ as $4^{2} \cdot 2$ .

Tap for more steps...

Step 1.8.1

Factor $16$ out of $32$ .

$5 \sqrt{2} + 6 \sqrt{2} + 4 \sqrt{2} + \sqrt{16 (2)}$

Step 1.8.2

Rewrite $16$ as $4^{2}$ .

$5 \sqrt{2} + 6 \sqrt{2} + 4 \sqrt{2} + \sqrt{4^{2} \cdot 2}$

Step 1.9

Pull terms out from under the radical.

$5 \sqrt{2} + 6 \sqrt{2} + 4 \sqrt{2} + 4 \sqrt{2}$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Add $5 \sqrt{2}$ and $6 \sqrt{2}$ .

$11 \sqrt{2} + 4 \sqrt{2} + 4 \sqrt{2}$

Step 2.2

Add $11 \sqrt{2}$ and $4 \sqrt{2}$ .

$15 \sqrt{2} + 4 \sqrt{2}$

Step 2.3

Add $15 \sqrt{2}$ and $4 \sqrt{2}$ .

$19 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$19 \sqrt{2}$

Decimal Form:

$26.87005768 \dots$