Solve 1/2sqrt{2-1/4}

$$\frac{ 1 }{ 2 } \sqrt{ 2- \frac{ 1 }{ 4 } }$$

Evaluate

$$\frac{\sqrt{7}}{4}\approx 0.661437828$$

Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$\frac{1}{2}\sqrt{\frac{8}{4}-\frac{1}{4}}$$

Since \frac{8}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\sqrt{\frac{8-1}{4}}$$

Subtract 1 from 8 to get 7.

$$\frac{1}{2}\sqrt{\frac{7}{4}}$$

Rewrite the square root of the division \sqrt{\frac{7}{4}} as the division of square roots \frac{\sqrt{7}}{\sqrt{4}}.

$$\frac{1}{2}\times \frac{\sqrt{7}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{1}{2}\times \frac{\sqrt{7}}{2}$$

Multiply \frac{1}{2} times \frac{\sqrt{7}}{2} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{7}}{4}$$