Simplify the Radical Expression 3 square root of 12-5 square root of 27+2 square root of 75

$3 \sqrt{12} - 5 \sqrt{27} + 2 \sqrt{75}$

Step 1

Simplify each term.

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

Factor $4$ out of $12$ .

$3 \sqrt{4 (3)} - 5 \sqrt{27} + 2 \sqrt{75}$

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

$3 \sqrt{2^{2} \cdot 3} - 5 \sqrt{27} + 2 \sqrt{75}$

Pull terms out from under the radical.

$3 (| 2 | \sqrt{3}) - 5 \sqrt{27} + 2 \sqrt{75}$

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

$3 (2 \sqrt{3}) - 5 \sqrt{27} + 2 \sqrt{75}$

Multiply $2$ by $3$ .

$6 \sqrt{3} - 5 \sqrt{27} + 2 \sqrt{75}$

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

Factor $9$ out of $27$ .

$6 \sqrt{3} - 5 \sqrt{9 (3)} + 2 \sqrt{75}$

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

$6 \sqrt{3} - 5 \sqrt{3^{2} \cdot 3} + 2 \sqrt{75}$

Pull terms out from under the radical.

$6 \sqrt{3} - 5 (| 3 | \sqrt{3}) + 2 \sqrt{75}$

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

$6 \sqrt{3} - 5 (3 \sqrt{3}) + 2 \sqrt{75}$

Multiply $3$ by $- 5$ .

$6 \sqrt{3} - 15 \sqrt{3} + 2 \sqrt{75}$

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

Factor $25$ out of $75$ .

$6 \sqrt{3} - 15 \sqrt{3} + 2 \sqrt{25 (3)}$

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

$6 \sqrt{3} - 15 \sqrt{3} + 2 \sqrt{5^{2} \cdot 3}$

Pull terms out from under the radical.

$6 \sqrt{3} - 15 \sqrt{3} + 2 (| 5 | \sqrt{3})$

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

$6 \sqrt{3} - 15 \sqrt{3} + 2 (5 \sqrt{3})$

Multiply $5$ by $2$ .

$6 \sqrt{3} - 15 \sqrt{3} + 10 \sqrt{3}$

Step 2

Subtract $15 \sqrt{3}$ from $6 \sqrt{3}$ .

$- 9 \sqrt{3} + 10 \sqrt{3}$

Step 3

Add $- 9 \sqrt{3}$ and $10 \sqrt{3}$ .

$\sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$

Simplify the Radical Expression 3 square root of 12-5 square root of 27+2 square root of 75

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