Solve 1sqrt{2^2-1^2/4}div2

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

Evaluate

$$\frac{\sqrt{15}}{4}\approx 0.968245837$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Calculate 1 to the power of 2 and get 1.

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

Convert 4 to fraction \frac{16}{4}.

$$\frac{1\sqrt{\frac{16}{4}-\frac{1}{4}}}{2}$$

Since \frac{16}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1\sqrt{\frac{16-1}{4}}}{2}$$

Subtract 1 from 16 to get 15.

$$\frac{1\sqrt{\frac{15}{4}}}{2}$$

Rewrite the square root of the division \sqrt{\frac{15}{4}} as the division of square roots \frac{\sqrt{15}}{\sqrt{4}}.

$$\frac{1\times \frac{\sqrt{15}}{\sqrt{4}}}{2}$$

Calculate the square root of 4 and get 2.

$$\frac{1\times \frac{\sqrt{15}}{2}}{2}$$

Express 1\times \frac{\sqrt{15}}{2} as a single fraction.

$$\frac{\frac{\sqrt{15}}{2}}{2}$$

Express \frac{\frac{\sqrt{15}}{2}}{2} as a single fraction.

$$\frac{\sqrt{15}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{15}}{4}$$