Evaluate square root of 200- square root of 72

$\sqrt{200} - \sqrt{72}$

Step 1

Simplify each term.

Rewrite $200$ as $10^{2} \cdot 2$ .

Factor $100$ out of $200$ .

$\sqrt{100 (2)} - \sqrt{72}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 2} - \sqrt{72}$

$\sqrt{10^{2} \cdot 2} - \sqrt{72}$

Pull terms out from under the radical.

$10 \sqrt{2} - \sqrt{72}$

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

Factor $36$ out of $72$ .

$10 \sqrt{2} - \sqrt{36 (2)}$

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

$10 \sqrt{2} - \sqrt{6^{2} \cdot 2}$

$10 \sqrt{2} - \sqrt{6^{2} \cdot 2}$

Pull terms out from under the radical.

$10 \sqrt{2} - (6 \sqrt{2})$

Multiply $6$ by $- 1$ .

$10 \sqrt{2} - 6 \sqrt{2}$

$10 \sqrt{2} - 6 \sqrt{2}$

Step 2

Subtract $6 \sqrt{2}$ from $10 \sqrt{2}$ .

$4 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{2}$

Decimal Form:

$5.65685424 \dots$

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