Evaluate 6 square root of 75-3 square root of 50+ square root of 12

$6 \sqrt{75} - 3 \sqrt{50} + \sqrt{12}$

Step 1

Simplify each term.

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

Factor $25$ out of $75$ .

$6 \sqrt{25 (3)} - 3 \sqrt{50} + \sqrt{12}$

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

$6 \sqrt{5^{2} \cdot 3} - 3 \sqrt{50} + \sqrt{12}$

Pull terms out from under the radical.

$6 (5 \sqrt{3}) - 3 \sqrt{50} + \sqrt{12}$

Multiply $5$ by $6$ .

$30 \sqrt{3} - 3 \sqrt{50} + \sqrt{12}$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$30 \sqrt{3} - 3 \sqrt{25 (2)} + \sqrt{12}$

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

$30 \sqrt{3} - 3 \sqrt{5^{2} \cdot 2} + \sqrt{12}$

Pull terms out from under the radical.

$30 \sqrt{3} - 3 (5 \sqrt{2}) + \sqrt{12}$

Multiply $5$ by $- 3$ .

$30 \sqrt{3} - 15 \sqrt{2} + \sqrt{12}$

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

Factor $4$ out of $12$ .

$30 \sqrt{3} - 15 \sqrt{2} + \sqrt{4 (3)}$

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

$30 \sqrt{3} - 15 \sqrt{2} + \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$30 \sqrt{3} - 15 \sqrt{2} + 2 \sqrt{3}$

Step 2

Add $30 \sqrt{3}$ and $2 \sqrt{3}$ .

$32 \sqrt{3} - 15 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$32 \sqrt{3} - 15 \sqrt{2}$

Decimal Form:

$34.21242240 \dots$