Simplify the Radical Expression 2 square root of 12-3 square root of 75+ square root of 27

$2 \sqrt{12} - 3 \sqrt{75} + \sqrt{27}$

Step 1

Simplify each term.

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

Factor $4$ out of $12$ .

$2 \sqrt{4 (3)} - 3 \sqrt{75} + \sqrt{27}$

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

$2 \sqrt{2^{2} \cdot 3} - 3 \sqrt{75} + \sqrt{27}$

Pull terms out from under the radical.

$2 (| 2 | \sqrt{3}) - 3 \sqrt{75} + \sqrt{27}$

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

$2 (2 \sqrt{3}) - 3 \sqrt{75} + \sqrt{27}$

Multiply $2$ by $2$ .

$4 \sqrt{3} - 3 \sqrt{75} + \sqrt{27}$

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

Factor $25$ out of $75$ .

$4 \sqrt{3} - 3 \sqrt{25 (3)} + \sqrt{27}$

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

$4 \sqrt{3} - 3 \sqrt{5^{2} \cdot 3} + \sqrt{27}$

Pull terms out from under the radical.

$4 \sqrt{3} - 3 (| 5 | \sqrt{3}) + \sqrt{27}$

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

$4 \sqrt{3} - 3 (5 \sqrt{3}) + \sqrt{27}$

Multiply $5$ by $- 3$ .

$4 \sqrt{3} - 15 \sqrt{3} + \sqrt{27}$

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

Factor $9$ out of $27$ .

$4 \sqrt{3} - 15 \sqrt{3} + \sqrt{9 (3)}$

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

$4 \sqrt{3} - 15 \sqrt{3} + \sqrt{3^{2} \cdot 3}$

Pull terms out from under the radical.

$4 \sqrt{3} - 15 \sqrt{3} + | 3 | \sqrt{3}$

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

$4 \sqrt{3} - 15 \sqrt{3} + 3 \sqrt{3}$

Step 2

Subtract $15 \sqrt{3}$ from $4 \sqrt{3}$ .

$- 11 \sqrt{3} + 3 \sqrt{3}$

Step 3

Add $- 11 \sqrt{3}$ and $3 \sqrt{3}$ .

$- 8 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- 8 \sqrt{3}$

Decimal Form:

$- 13.85640646 \dots$

Simplify the Radical Expression 2 square root of 12-3 square root of 75+ square root of 27

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