Solve sqrt{24}-sqrt{1/2}

$$\sqrt { 24 } - \sqrt { \frac { 1 } { 2 } }$$

Evaluate

$$-\frac{\sqrt{2}}{2}+2\sqrt{6}\approx 4.191872704$$

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}.

$$2\sqrt{6}-\sqrt{\frac{1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$2\sqrt{6}-\frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$2\sqrt{6}-\frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$2\sqrt{6}-\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

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

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

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

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

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

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