Solve -5sqrt{22/7}

$$- 5 \sqrt { 2 \frac { 2 } { 7 } }$$

Evaluate

$$-\frac{20\sqrt{7}}{7}\approx -7.55928946$$

Solution Steps

Multiply 2 and 7 to get 14.

$$-5\sqrt{\frac{14+2}{7}}$$

Add 14 and 2 to get 16.

$$-5\sqrt{\frac{16}{7}}$$

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

$$-5\times \frac{\sqrt{16}}{\sqrt{7}}$$

Calculate the square root of 16 and get 4.

$$-5\times \frac{4}{\sqrt{7}}$$

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

$$-5\times \frac{4\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$-5\times \frac{4\sqrt{7}}{7}$$

Express -5\times \frac{4\sqrt{7}}{7} as a single fraction.

$$\frac{-5\times 4\sqrt{7}}{7}$$

Multiply -5 and 4 to get -20.

$$\frac{-20\sqrt{7}}{7}$$