Solve (sqrt{8}-sqrt{1/2})

$$( \sqrt { 8 } - \sqrt { \frac { 1 } { 2 } } )$$

Evaluate

$$\frac{3\sqrt{2}}{2}\approx 2.121320344$$

Short Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

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

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

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

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

Do the calculations in 4\sqrt{2}-\sqrt{2}.

$$\frac{3\sqrt{2}}{2}$$