Solve sqrt{1-{left(frac{5sqrt{3}}{14}right)}^2}

$$\sqrt{ 1- { \left( \frac{ 5 \sqrt{ 3 } }{ 14 } \right) }^{ 2 } }$$

Evaluate

$$\frac{11}{14}\approx 0.785714286$$

Solution Steps

To raise \frac{5\sqrt{3}}{14} to a power, raise both numerator and denominator to the power and then divide.

$$\sqrt{1-\frac{\left(5\sqrt{3}\right)^{2}}{14^{2}}}$$

Expand \left(5\sqrt{3}\right)^{2}.

$$\sqrt{1-\frac{5^{2}\left(\sqrt{3}\right)^{2}}{14^{2}}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{1-\frac{25\left(\sqrt{3}\right)^{2}}{14^{2}}}$$

The square of \sqrt{3} is 3.

$$\sqrt{1-\frac{25\times 3}{14^{2}}}$$

Multiply 25 and 3 to get 75.

$$\sqrt{1-\frac{75}{14^{2}}}$$

Calculate 14 to the power of 2 and get 196.

$$\sqrt{1-\frac{75}{196}}$$

Subtract \frac{75}{196} from 1 to get \frac{121}{196}.

$$\sqrt{\frac{121}{196}}$$

Rewrite the square root of the division \frac{121}{196} as the division of square roots \frac{\sqrt{121}}{\sqrt{196}}. Take the square root of both numerator and denominator.

$$\frac{11}{14}$$

Factor

$$\frac{11}{2 \cdot 7} = 0.7857142857142857$$