Solve sqrt{(1-(-frac{55/73))}}{2}

$$\frac{ \sqrt{ (1-(- \frac{ 55 }{ 73 } )) } }{ 2 }$$

Evaluate

$$\frac{4\sqrt{146}}{73}\approx 0.662084711$$

Solution Steps

The opposite of -\frac{55}{73} is \frac{55}{73}.

$$\frac{\sqrt{1+\frac{55}{73}}}{2}$$

Convert 1 to fraction \frac{73}{73}.

$$\frac{\sqrt{\frac{73}{73}+\frac{55}{73}}}{2}$$

Since \frac{73}{73} and \frac{55}{73} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{\frac{73+55}{73}}}{2}$$

Add 73 and 55 to get 128.

$$\frac{\sqrt{\frac{128}{73}}}{2}$$

Rewrite the square root of the division \sqrt{\frac{128}{73}} as the division of square roots \frac{\sqrt{128}}{\sqrt{73}}.

$$\frac{\frac{\sqrt{128}}{\sqrt{73}}}{2}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$\frac{\frac{8\sqrt{2}}{\sqrt{73}}}{2}$$

Rationalize the denominator of \frac{8\sqrt{2}}{\sqrt{73}} by multiplying numerator and denominator by \sqrt{73}.

$$\frac{\frac{8\sqrt{2}\sqrt{73}}{\left(\sqrt{73}\right)^{2}}}{2}$$

The square of \sqrt{73} is 73.

$$\frac{\frac{8\sqrt{2}\sqrt{73}}{73}}{2}$$

To multiply \sqrt{2} and \sqrt{73}, multiply the numbers under the square root.

$$\frac{\frac{8\sqrt{146}}{73}}{2}$$

Express \frac{\frac{8\sqrt{146}}{73}}{2} as a single fraction.

$$\frac{8\sqrt{146}}{73\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{4\sqrt{146}}{73}$$