Evaluate 4 square root of 75-3 square root of 50+ square root of 27

$4 \sqrt{75} - 3 \sqrt{50} + \sqrt{27}$

Step 1

Simplify each term.

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

Factor $25$ out of $75$ .

$4 \sqrt{25 (3)} - 3 \sqrt{50} + \sqrt{27}$

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

$4 \sqrt{5^{2} \cdot 3} - 3 \sqrt{50} + \sqrt{27}$

Pull terms out from under the radical.

$4 (5 \sqrt{3}) - 3 \sqrt{50} + \sqrt{27}$

Multiply $5$ by $4$ .

$20 \sqrt{3} - 3 \sqrt{50} + \sqrt{27}$

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

Factor $25$ out of $50$ .

$20 \sqrt{3} - 3 \sqrt{25 (2)} + \sqrt{27}$

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

$20 \sqrt{3} - 3 \sqrt{5^{2} \cdot 2} + \sqrt{27}$

Pull terms out from under the radical.

$20 \sqrt{3} - 3 (5 \sqrt{2}) + \sqrt{27}$

Multiply $5$ by $- 3$ .

$20 \sqrt{3} - 15 \sqrt{2} + \sqrt{27}$

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

Factor $9$ out of $27$ .

$20 \sqrt{3} - 15 \sqrt{2} + \sqrt{9 (3)}$

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

$20 \sqrt{3} - 15 \sqrt{2} + \sqrt{3^{2} \cdot 3}$

Pull terms out from under the radical.

$20 \sqrt{3} - 15 \sqrt{2} + 3 \sqrt{3}$

Step 2

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

$23 \sqrt{3} - 15 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$23 \sqrt{3} - 15 \sqrt{2}$

Decimal Form:

$18.62396513 \dots$