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

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

Evaluate

$$\frac{\sqrt{3}}{16}\approx 0.108253175$$

Solution Steps

Multiply \frac{1}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 1}{4\times 2}.

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

Convert 1 to fraction \frac{4}{4}.

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

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

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

Subtract 1 from 4 to get 3.

$$\frac{1}{8}\sqrt{\frac{3}{4}}$$

Rewrite the square root of the division \sqrt{\frac{3}{4}} as the division of square roots \frac{\sqrt{3}}{\sqrt{4}}.

$$\frac{1}{8}\times \frac{\sqrt{3}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{1}{8}\times \frac{\sqrt{3}}{2}$$

Multiply \frac{1}{8} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{3}}{8\times 2}$$

Multiply 8 and 2 to get 16.

$$\frac{\sqrt{3}}{16}$$