Algebra Examples

$\sqrt{75} - \sqrt{27}$

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 $75$ .

$\sqrt{25 (3)} - \sqrt{27}$

Step 1.1.2

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

$\sqrt{5^{2} \cdot 3} - \sqrt{27}$

Step 1.2

Pull terms out from under the radical.

$| 5 | \sqrt{3} - \sqrt{27}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$5 \sqrt{3} - \sqrt{27}$

Step 1.4

Rewrite $27$ as $3^{2} \cdot 3$ .

Tap for more steps...

Step 1.4.1

Factor $9$ out of $27$ .

$5 \sqrt{3} - \sqrt{9 (3)}$

Step 1.4.2

Rewrite $9$ as $3^{2}$ .

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

Step 1.5

Pull terms out from under the radical.

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

Step 1.6

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

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

Step 1.7

Multiply $3$ by $- 1$ .

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

Step 2

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

$2 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3}$

Decimal Form:

$3.46410161 \dots$