Evaluate square root of 72+ square root of 50- square root of 8

$\sqrt{72} + \sqrt{50} - \sqrt{8}$

Step 1

Simplify each term.

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

Factor $36$ out of $72$ .

$\sqrt{36 (2)} + \sqrt{50} - \sqrt{8}$

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

$\sqrt{6^{2} \cdot 2} + \sqrt{50} - \sqrt{8}$

$\sqrt{6^{2} \cdot 2} + \sqrt{50} - \sqrt{8}$

Pull terms out from under the radical.

$6 \sqrt{2} + \sqrt{50} - \sqrt{8}$

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

Factor $25$ out of $50$ .

$6 \sqrt{2} + \sqrt{25 (2)} - \sqrt{8}$

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

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

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

Pull terms out from under the radical.

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

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

Factor $4$ out of $8$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

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

Step 2

Simplify by adding terms.

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

$11 \sqrt{2} - 2 \sqrt{2}$

Subtract $2 \sqrt{2}$ from $11 \sqrt{2}$ .

$9 \sqrt{2}$

$9 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{2}$

Decimal Form:

$12.72792206 \dots$

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