Evaluate 3 square root of 27-5 square root of 12+4 square root of 75

$3 \sqrt{27} - 5 \sqrt{12} + 4 \sqrt{75}$

Step 1

Simplify each term.

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

Factor $9$ out of $27$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $3$ .

$9 \sqrt{3} - 5 \sqrt{12} + 4 \sqrt{75}$

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

Factor $4$ out of $12$ .

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

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

$9 \sqrt{3} - 5 \sqrt{2^{2} \cdot 3} + 4 \sqrt{75}$

Pull terms out from under the radical.

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

Multiply $2$ by $- 5$ .

$9 \sqrt{3} - 10 \sqrt{3} + 4 \sqrt{75}$

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

Factor $25$ out of $75$ .

$9 \sqrt{3} - 10 \sqrt{3} + 4 \sqrt{25 (3)}$

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

$9 \sqrt{3} - 10 \sqrt{3} + 4 \sqrt{5^{2} \cdot 3}$

Pull terms out from under the radical.

$9 \sqrt{3} - 10 \sqrt{3} + 4 (5 \sqrt{3})$

Multiply $5$ by $4$ .

$9 \sqrt{3} - 10 \sqrt{3} + 20 \sqrt{3}$

Step 2

Simplify by adding terms.

Subtract $10 \sqrt{3}$ from $9 \sqrt{3}$ .

$- \sqrt{3} + 20 \sqrt{3}$

Add $- \sqrt{3}$ and $20 \sqrt{3}$ .

$19 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$19 \sqrt{3}$

Decimal Form:

$32.90896534 \dots$