Evaluate |2 square root of 3-4|-3 square root of 12+ square root of 48+3

$| 2 \sqrt{3} - 4 | - 3 \sqrt{12} + \sqrt{48} + 3$

Simplify each term.

Tap for more steps…

$2 \sqrt{3} - 4$ is approximately $- 0.53589838$ which is negative so negate $2 \sqrt{3} - 4$ and remove the absolute value

$- (2 \sqrt{3} - 4) - 3 \sqrt{12} + \sqrt{48} + 3$

Apply the distributive property.

$- (2 \sqrt{3}) - - 4 - 3 \sqrt{12} + \sqrt{48} + 3$

Multiply $2$ by $- 1$ .

$- 2 \sqrt{3} - - 4 - 3 \sqrt{12} + \sqrt{48} + 3$

Multiply $- 1$ by $- 4$ .

$- 2 \sqrt{3} + 4 - 3 \sqrt{12} + \sqrt{48} + 3$

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

Tap for more steps…

Factor $4$ out of $12$ .

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

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

$- 2 \sqrt{3} + 4 - 3 \sqrt{2^{2} \cdot 3} + \sqrt{48} + 3$

Pull terms out from under the radical.

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

Multiply $2$ by $- 3$ .

$- 2 \sqrt{3} + 4 - 6 \sqrt{3} + \sqrt{48} + 3$

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

Tap for more steps…

Factor $16$ out of $48$ .

$- 2 \sqrt{3} + 4 - 6 \sqrt{3} + \sqrt{16 (3)} + 3$

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

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

Pull terms out from under the radical.

$- 2 \sqrt{3} + 4 - 6 \sqrt{3} + 4 \sqrt{3} + 3$

Simplify by adding terms.

Tap for more steps…

Subtract $6 \sqrt{3}$ from $- 2 \sqrt{3}$ .

$4 - 8 \sqrt{3} + 4 \sqrt{3} + 3$

Add $4$ and $3$ .

$7 - 8 \sqrt{3} + 4 \sqrt{3}$

Add $- 8 \sqrt{3}$ and $4 \sqrt{3}$ .

$7 - 4 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$7 - 4 \sqrt{3}$

Decimal Form:

$0.07179676 \dots$

Evaluate |2 square root of 3-4|-3 square root of 12+ square root of 48+3

Meet the Team our Math Expers

Our Professionals

Robert Kristofer

Anna Frok

Magnus Flores

Lydia Fran

We are MathExperts

We can solve all your math problems