Solve sqrt{4-(2/7sqrt{21})^2}

$$\sqrt { 4 - ( \frac { 2 } { 7 } \sqrt { 21 } ) ^ { 2 } }$$

Evaluate

$$\frac{4\sqrt{7}}{7}\approx 1.511857892$$

Solution Steps

Expand \left(\frac{2}{7}\sqrt{21}\right)^{2}.

$$\sqrt{4-\left(\frac{2}{7}\right)^{2}\left(\sqrt{21}\right)^{2}}$$

Calculate \frac{2}{7} to the power of 2 and get \frac{4}{49}.

$$\sqrt{4-\frac{4}{49}\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$\sqrt{4-\frac{4}{49}\times 21}$$

Multiply \frac{4}{49} and 21 to get \frac{12}{7}.

$$\sqrt{4-\frac{12}{7}}$$

Subtract \frac{12}{7} from 4 to get \frac{16}{7}.

$$\sqrt{\frac{16}{7}}$$

Rewrite the square root of the division \sqrt{\frac{16}{7}} as the division of square roots \frac{\sqrt{16}}{\sqrt{7}}.

$$\frac{\sqrt{16}}{\sqrt{7}}$$

Calculate the square root of 16 and get 4.

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

Rationalize the denominator of \frac{4}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{4\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

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