Solve 8sqrt{100/149}

$$8 \sqrt { \frac { 100 } { 149 } }$$

Evaluate

$$\frac{80\sqrt{149}}{149}\approx 6.553855364$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{100}{149}} as the division of square roots \frac{\sqrt{100}}{\sqrt{149}}.

$$8\times \frac{\sqrt{100}}{\sqrt{149}}$$

Calculate the square root of 100 and get 10.

$$8\times \frac{10}{\sqrt{149}}$$

Rationalize the denominator of \frac{10}{\sqrt{149}} by multiplying numerator and denominator by \sqrt{149}.

$$8\times \frac{10\sqrt{149}}{\left(\sqrt{149}\right)^{2}}$$

The square of \sqrt{149} is 149.

$$8\times \frac{10\sqrt{149}}{149}$$

Express 8\times \frac{10\sqrt{149}}{149} as a single fraction.

$$\frac{8\times 10\sqrt{149}}{149}$$

Multiply 8 and 10 to get 80.

$$\frac{80\sqrt{149}}{149}$$