Simplify the Radical Expression 4 square root of 27-2 square root of 12-5 square root of 75

$4 \sqrt{27} - 2 \sqrt{12} - 5 \sqrt{75}$

Step 1

Simplify each term.

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

Factor $9$ out of $27$ .

$4 \sqrt{9 (3)} - 2 \sqrt{12} - 5 \sqrt{75}$

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

$4 \sqrt{3^{2} \cdot 3} - 2 \sqrt{12} - 5 \sqrt{75}$

Pull terms out from under the radical.

$4 (| 3 | \sqrt{3}) - 2 \sqrt{12} - 5 \sqrt{75}$

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

$4 (3 \sqrt{3}) - 2 \sqrt{12} - 5 \sqrt{75}$

Multiply $3$ by $4$ .

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

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

Factor $4$ out of $12$ .

$12 \sqrt{3} - 2 \sqrt{4 (3)} - 5 \sqrt{75}$

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

$12 \sqrt{3} - 2 \sqrt{2^{2} \cdot 3} - 5 \sqrt{75}$

Pull terms out from under the radical.

$12 \sqrt{3} - 2 (| 2 | \sqrt{3}) - 5 \sqrt{75}$

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

$12 \sqrt{3} - 2 (2 \sqrt{3}) - 5 \sqrt{75}$

Multiply $2$ by $- 2$ .

$12 \sqrt{3} - 4 \sqrt{3} - 5 \sqrt{75}$

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

Factor $25$ out of $75$ .

$12 \sqrt{3} - 4 \sqrt{3} - 5 \sqrt{25 (3)}$

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

$12 \sqrt{3} - 4 \sqrt{3} - 5 \sqrt{5^{2} \cdot 3}$

Pull terms out from under the radical.

$12 \sqrt{3} - 4 \sqrt{3} - 5 (| 5 | \sqrt{3})$

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

$12 \sqrt{3} - 4 \sqrt{3} - 5 (5 \sqrt{3})$

Multiply $5$ by $- 5$ .

$12 \sqrt{3} - 4 \sqrt{3} - 25 \sqrt{3}$

Step 2

Subtract $4 \sqrt{3}$ from $12 \sqrt{3}$ .

$8 \sqrt{3} - 25 \sqrt{3}$

Step 3

Subtract $25 \sqrt{3}$ from $8 \sqrt{3}$ .

$- 17 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- 17 \sqrt{3}$

Decimal Form:

$- 29.44486372 \dots$

Simplify the Radical Expression 4 square root of 27-2 square root of 12-5 square root of 75

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