Solve sqrt{24}-frac{sqrt{7}}{2}

$$\sqrt { 24 } - \frac { \sqrt { 7 } } { 2 }$$

Evaluate

$$-\frac{\sqrt{7}}{2}+2\sqrt{6}\approx 3.57610383$$

Short Solution Steps

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}.

$$2\sqrt{6}-\frac{\sqrt{7}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\sqrt{6} times \frac{2}{2}.

$$\frac{2\times 2\sqrt{6}}{2}-\frac{\sqrt{7}}{2}$$

Since \frac{2\times 2\sqrt{6}}{2} and \frac{\sqrt{7}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2\sqrt{6}-\sqrt{7}}{2}$$

Do the multiplications in 2\times 2\sqrt{6}-\sqrt{7}.

$$\frac{4\sqrt{6}-\sqrt{7}}{2}$$

Factor

$$\frac{4 \sqrt{6} - \sqrt{7}}{2} = 3.5761038300340604$$