Solve 1/sqrt{(frac{55{2})^2-1(-1/2)}}

$$\frac { 1 } { \sqrt { ( \frac { 55 } { 2 } ) ^ { 2 } - 1 ( - \frac { 1 } { 2 } ) } }$$

Evaluate

$$\frac{2\sqrt{3027}}{3027}\approx 0.036351621$$

Solution Steps

Calculate \frac{55}{2} to the power of 2 and get \frac{3025}{4}.

$$\frac{1}{\sqrt{\frac{3025}{4}-1\left(-\frac{1}{2}\right)}}$$

Multiply 1 and -\frac{1}{2} to get -\frac{1}{2}.

$$\frac{1}{\sqrt{\frac{3025}{4}-\left(-\frac{1}{2}\right)}}$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{1}{\sqrt{\frac{3025}{4}+\frac{1}{2}}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{3025}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{1}{\sqrt{\frac{3025}{4}+\frac{2}{4}}}$$

Since \frac{3025}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{1}{\sqrt{\frac{3025+2}{4}}}$$

Add 3025 and 2 to get 3027.

$$\frac{1}{\sqrt{\frac{3027}{4}}}$$

Rewrite the square root of the division \sqrt{\frac{3027}{4}} as the division of square roots \frac{\sqrt{3027}}{\sqrt{4}}.

$$\frac{1}{\frac{\sqrt{3027}}{\sqrt{4}}}$$

Calculate the square root of 4 and get 2.

$$\frac{1}{\frac{\sqrt{3027}}{2}}$$

Divide 1 by \frac{\sqrt{3027}}{2} by multiplying 1 by the reciprocal of \frac{\sqrt{3027}}{2}.

$$\frac{2}{\sqrt{3027}}$$

Rationalize the denominator of \frac{2}{\sqrt{3027}} by multiplying numerator and denominator by \sqrt{3027}.

$$\frac{2\sqrt{3027}}{\left(\sqrt{3027}\right)^{2}}$$

The square of \sqrt{3027} is 3027.

$$\frac{2\sqrt{3027}}{3027}$$