Evaluate square root of 72- square root of 50

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

Step 1

Simplify each term.

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

Factor $36$ out of $72$ .

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

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

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

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

Pull terms out from under the radical.

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

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

Factor $25$ out of $50$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $5$ by $- 1$ .

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

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

Step 2

Subtract $5 \sqrt{2}$ from $6 \sqrt{2}$ .

$\sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$

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