Simplify the Radical Expression square root of 75+2 square root of 12-5 square root of 3

$\sqrt{75} + 2 \sqrt{12} - 5 \sqrt{3}$

Simplify each term.

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

Factor $25$ out of $75$ .

$\sqrt{25 (3)} + 2 \sqrt{12} - 5 \sqrt{3}$

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

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

Pull terms out from under the radical.

$| 5 | \sqrt{3} + 2 \sqrt{12} - 5 \sqrt{3}$

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

$5 \sqrt{3} + 2 \sqrt{12} - 5 \sqrt{3}$

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

Factor $4$ out of $12$ .

$5 \sqrt{3} + 2 \sqrt{4 (3)} - 5 \sqrt{3}$

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

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

Pull terms out from under the radical.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Multiply $2$ by $2$ .

$5 \sqrt{3} + 4 \sqrt{3} - 5 \sqrt{3}$

Add $5 \sqrt{3}$ and $4 \sqrt{3}$ .

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

Subtract $5 \sqrt{3}$ from $9 \sqrt{3}$ .

$4 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{3}$

Decimal Form:

$6.92820323 \dots$