Simplify 3 square root of 24x-2 square root of 54x+ square root of 48

$3 \sqrt{24 x} - 2 \sqrt{54 x} + \sqrt{48}$

Step 1

Simplify each term.

Rewrite $24 x$ as $2^{2} \cdot (6 x)$ .

Factor $4$ out of $24$ .

$3 \sqrt{4 (6) x} - 2 \sqrt{54 x} + \sqrt{48}$

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

$3 \sqrt{2^{2} \cdot 6 x} - 2 \sqrt{54 x} + \sqrt{48}$

Add parentheses.

$3 \sqrt{2^{2} \cdot (6 x)} - 2 \sqrt{54 x} + \sqrt{48}$

Pull terms out from under the radical.

$3 (2 \sqrt{6 x}) - 2 \sqrt{54 x} + \sqrt{48}$

Multiply $2$ by $3$ .

$6 \sqrt{6 x} - 2 \sqrt{54 x} + \sqrt{48}$

Rewrite $54 x$ as $3^{2} \cdot (6 x)$ .

Factor $9$ out of $54$ .

$6 \sqrt{6 x} - 2 \sqrt{9 (6) x} + \sqrt{48}$

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

$6 \sqrt{6 x} - 2 \sqrt{3^{2} \cdot 6 x} + \sqrt{48}$

Add parentheses.

$6 \sqrt{6 x} - 2 \sqrt{3^{2} \cdot (6 x)} + \sqrt{48}$

Pull terms out from under the radical.

$6 \sqrt{6 x} - 2 (3 \sqrt{6 x}) + \sqrt{48}$

Multiply $3$ by $- 2$ .

$6 \sqrt{6 x} - 6 \sqrt{6 x} + \sqrt{48}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$6 \sqrt{6 x} - 6 \sqrt{6 x} + \sqrt{16 (3)}$

Rewrite $16$ as $4^{2}$ .

$6 \sqrt{6 x} - 6 \sqrt{6 x} + \sqrt{4^{2} \cdot 3}$

Pull terms out from under the radical.

$6 \sqrt{6 x} - 6 \sqrt{6 x} + 4 \sqrt{3}$

Step 2

Simplify by adding terms.

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

$0 + 4 \sqrt{3}$

Add $0$ and $4 \sqrt{3}$ .

$4 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{3}$

Decimal Form:

$6.92820323 \dots$