Simplify 3 square root of 4x- square root of 9x+5 square root of 27- square root of x

$3 \sqrt{4 x} - \sqrt{9 x} + 5 \sqrt{27} - \sqrt{x}$

Step 1

Simplify each term.

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

$3 \sqrt{2^{2} x} - \sqrt{9 x} + 5 \sqrt{27} - \sqrt{x}$

Pull terms out from under the radical.

$3 (2 \sqrt{x}) - \sqrt{9 x} + 5 \sqrt{27} - \sqrt{x}$

Multiply $2$ by $3$ .

$6 \sqrt{x} - \sqrt{9 x} + 5 \sqrt{27} - \sqrt{x}$

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

$6 \sqrt{x} - \sqrt{3^{2} x} + 5 \sqrt{27} - \sqrt{x}$

Pull terms out from under the radical.

$6 \sqrt{x} - (3 \sqrt{x}) + 5 \sqrt{27} - \sqrt{x}$

Multiply $3$ by $- 1$ .

$6 \sqrt{x} - 3 \sqrt{x} + 5 \sqrt{27} - \sqrt{x}$

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

Factor $9$ out of $27$ .

$6 \sqrt{x} - 3 \sqrt{x} + 5 \sqrt{9 (3)} - \sqrt{x}$

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $5$ .

$6 \sqrt{x} - 3 \sqrt{x} + 15 \sqrt{3} - \sqrt{x}$

Step 2

Simplify by adding terms.

Subtract $3 \sqrt{x}$ from $6 \sqrt{x}$ .

$3 \sqrt{x} + 15 \sqrt{3} - \sqrt{x}$

Subtract $\sqrt{x}$ from $3 \sqrt{x}$ .

$2 \sqrt{x} + 15 \sqrt{3}$