Solve 4-1/2*sqrt{12}+sqrt{24}

$$4- \frac{ 1 }{ 2 } \times \sqrt{ 12 } + \sqrt{ 24 }$$

Evaluate

$$2\sqrt{6}+4-\sqrt{3}\approx 7.166928678$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$4-\frac{1}{2}\times 2\sqrt{3}+\sqrt{24}$$

Cancel out 2 and 2.

$$4-\sqrt{3}+\sqrt{24}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

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

Factor

$$2 \sqrt{6} + 4 - \sqrt{3} = 7.166928678$$