Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Add $144$ and $25$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

Multiply $- 1$ by $12$ .

$13 - 12 - \sqrt{25}$

Step 1.7

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

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

Step 1.8

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

$13 - 12 - 1 \cdot 5$

Step 1.9

Multiply $- 1$ by $5$ .

$13 - 12 - 5$

Step 2

Simplify by subtracting numbers.

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Step 2.1

Subtract $12$ from $13$ .

$1 - 5$

Step 2.2

Subtract $5$ from $1$ .

$- 4$