Precalculus Examples

$\sqrt{75} - \sqrt{12}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $75$ as $5^{2} \cdot 3$ .

Tap for more steps...

Step 1.1.1

Factor $25$ out of $75$ .

$\sqrt{25 (3)} - \sqrt{12}$

Step 1.1.2

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

$\sqrt{5^{2} \cdot 3} - \sqrt{12}$

$\sqrt{5^{2} \cdot 3} - \sqrt{12}$

Step 1.2

Pull terms out from under the radical.

$5 \sqrt{3} - \sqrt{12}$

Step 1.3

Rewrite $12$ as $2^{2} \cdot 3$ .

Tap for more steps...

Step 1.3.1

Factor $4$ out of $12$ .

$5 \sqrt{3} - \sqrt{4 (3)}$

Step 1.3.2

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

$5 \sqrt{3} - \sqrt{2^{2} \cdot 3}$

$5 \sqrt{3} - \sqrt{2^{2} \cdot 3}$

Step 1.4

Pull terms out from under the radical.

$5 \sqrt{3} - (2 \sqrt{3})$

Step 1.5

Multiply $2$ by $- 1$ .

$5 \sqrt{3} - 2 \sqrt{3}$

$5 \sqrt{3} - 2 \sqrt{3}$

Step 2

Subtract $2 \sqrt{3}$ from $5 \sqrt{3}$ .

$3 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{3}$

Decimal Form:

$5.19615242 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$