Evaluate square root of 144+25- square root of 144- square root of 25

$\sqrt{144 + 25} - \sqrt{144} - \sqrt{25}$

Simplify each term.

Add $144$ and $25$ .

$\sqrt{169} - \sqrt{144} - \sqrt{25}$

Rewrite $169$ as $13^{2}$ .

$\sqrt{13^{2}} - \sqrt{144} - \sqrt{25}$

Pull terms out from under the radical, assuming positive real numbers.

$13 - \sqrt{144} - \sqrt{25}$

Rewrite $144$ as $12^{2}$ .

$13 - \sqrt{12^{2}} - \sqrt{25}$

Pull terms out from under the radical, assuming positive real numbers.

$13 - 1 \cdot 12 - \sqrt{25}$

Multiply $- 1$ by $12$ .

$13 - 12 - \sqrt{25}$

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

$13 - 12 - \sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$13 - 12 - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$13 - 12 - 5$

Simplify by subtracting numbers.

Subtract $12$ from $13$ .

$1 - 5$

Subtract $5$ from $1$ .

$- 4$