Solve 1/sqrt{1+frac{7{4}}}

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

Evaluate

$$\frac{2\sqrt{11}}{11}\approx 0.603022689$$

Solution Steps

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

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

Since \frac{4}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

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

Add 4 and 7 to get 11.

$$\frac{1}{\sqrt{\frac{11}{4}}}$$

Rewrite the square root of the division \sqrt{\frac{11}{4}} as the division of square roots \frac{\sqrt{11}}{\sqrt{4}}.

$$\frac{1}{\frac{\sqrt{11}}{\sqrt{4}}}$$

Calculate the square root of 4 and get 2.

$$\frac{1}{\frac{\sqrt{11}}{2}}$$

Divide 1 by \frac{\sqrt{11}}{2} by multiplying 1 by the reciprocal of \frac{\sqrt{11}}{2}.

$$\frac{2}{\sqrt{11}}$$

Rationalize the denominator of \frac{2}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{2\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\frac{2\sqrt{11}}{11}$$