Simplify 2 square root of 27x+ square root of 75x+5 square root of 12x

$2 \sqrt{27 x} + \sqrt{75 x} + 5 \sqrt{12 x}$

Step 1

Simplify each term.

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

Factor $9$ out of $27$ .

$2 \sqrt{9 (3) x} + \sqrt{75 x} + 5 \sqrt{12 x}$

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

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

Add parentheses.

$2 \sqrt{3^{2} \cdot (3 x)} + \sqrt{75 x} + 5 \sqrt{12 x}$

Pull terms out from under the radical.

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

Multiply $3$ by $2$ .

$6 \sqrt{3 x} + \sqrt{75 x} + 5 \sqrt{12 x}$

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

Factor $25$ out of $75$ .

$6 \sqrt{3 x} + \sqrt{25 (3) x} + 5 \sqrt{12 x}$

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

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

Add parentheses.

$6 \sqrt{3 x} + \sqrt{5^{2} \cdot (3 x)} + 5 \sqrt{12 x}$

Pull terms out from under the radical.

$6 \sqrt{3 x} + 5 \sqrt{3 x} + 5 \sqrt{12 x}$

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

Factor $4$ out of $12$ .

$6 \sqrt{3 x} + 5 \sqrt{3 x} + 5 \sqrt{4 (3) x}$

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

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

Add parentheses.

$6 \sqrt{3 x} + 5 \sqrt{3 x} + 5 \sqrt{2^{2} \cdot (3 x)}$

Pull terms out from under the radical.

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

Multiply $2$ by $5$ .

$6 \sqrt{3 x} + 5 \sqrt{3 x} + 10 \sqrt{3 x}$

Step 2

Simplify by adding terms.

Add $6 \sqrt{3 x}$ and $5 \sqrt{3 x}$ .

$11 \sqrt{3 x} + 10 \sqrt{3 x}$

Add $11 \sqrt{3 x}$ and $10 \sqrt{3 x}$ .

$21 \sqrt{3 x}$