Solve sqrt{8div0.115}

$$\sqrt{ 8 \div 0.115 }$$

Evaluate

$$\frac{40\sqrt{23}}{23}\approx 8.340576562$$

Solution Steps

Expand \frac{8}{0.115} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{8000}{115}}$$

Reduce the fraction \frac{8000}{115} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{1600}{23}}$$

Rewrite the square root of the division \sqrt{\frac{1600}{23}} as the division of square roots \frac{\sqrt{1600}}{\sqrt{23}}.

$$\frac{\sqrt{1600}}{\sqrt{23}}$$

Calculate the square root of 1600 and get 40.

$$\frac{40}{\sqrt{23}}$$

Rationalize the denominator of \frac{40}{\sqrt{23}} by multiplying numerator and denominator by \sqrt{23}.

$$\frac{40\sqrt{23}}{\left(\sqrt{23}\right)^{2}}$$

The square of \sqrt{23} is 23.

$$\frac{40\sqrt{23}}{23}$$