Solve sqrt{1-(frac{4sqrt{19}}{19})^2}

$$\sqrt { 1 - ( \frac { 4 \sqrt { 19 } } { 19 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{57}}{19}\approx 0.397359707$$

Solution Steps

To raise \frac{4\sqrt{19}}{19} to a power, raise both numerator and denominator to the power and then divide.

$$\sqrt{1-\frac{\left(4\sqrt{19}\right)^{2}}{19^{2}}}$$

Expand \left(4\sqrt{19}\right)^{2}.

$$\sqrt{1-\frac{4^{2}\left(\sqrt{19}\right)^{2}}{19^{2}}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{1-\frac{16\left(\sqrt{19}\right)^{2}}{19^{2}}}$$

The square of \sqrt{19} is 19.

$$\sqrt{1-\frac{16\times 19}{19^{2}}}$$

Multiply 16 and 19 to get 304.

$$\sqrt{1-\frac{304}{19^{2}}}$$

Calculate 19 to the power of 2 and get 361.

$$\sqrt{1-\frac{304}{361}}$$

Reduce the fraction \frac{304}{361} to lowest terms by extracting and canceling out 19.

$$\sqrt{1-\frac{16}{19}}$$

Subtract \frac{16}{19} from 1 to get \frac{3}{19}.

$$\sqrt{\frac{3}{19}}$$

Rewrite the square root of the division \sqrt{\frac{3}{19}} as the division of square roots \frac{\sqrt{3}}{\sqrt{19}}.

$$\frac{\sqrt{3}}{\sqrt{19}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.

$$\frac{\sqrt{3}\sqrt{19}}{\left(\sqrt{19}\right)^{2}}$$

The square of \sqrt{19} is 19.

$$\frac{\sqrt{3}\sqrt{19}}{19}$$

To multiply \sqrt{3} and \sqrt{19}, multiply the numbers under the square root.

$$\frac{\sqrt{57}}{19}$$