Solve 0.35-0.38/sqrt{frac{0.38*0.62{700}}}

$$\frac{ 0.35-0.38 }{ \sqrt{ \frac{ 0.38 \times 0.62 }{ 700 } } }$$

Evaluate

$$-\frac{15\sqrt{4123}}{589}\approx -1.635244254$$

Solution Steps

Subtract 0.38 from 0.35 to get -0.03.

$$\frac{-0.03}{\sqrt{\frac{0.38\times 0.62}{700}}}$$

Multiply 0.38 and 0.62 to get 0.2356.

$$\frac{-0.03}{\sqrt{\frac{0.2356}{700}}}$$

Expand \frac{0.2356}{700} by multiplying both numerator and the denominator by 10000.

$$\frac{-0.03}{\sqrt{\frac{2356}{7000000}}}$$

Reduce the fraction \frac{2356}{7000000} to lowest terms by extracting and canceling out 4.

$$\frac{-0.03}{\sqrt{\frac{589}{1750000}}}$$

Rewrite the square root of the division \sqrt{\frac{589}{1750000}} as the division of square roots \frac{\sqrt{589}}{\sqrt{1750000}}.

$$\frac{-0.03}{\frac{\sqrt{589}}{\sqrt{1750000}}}$$

Factor 1750000=500^{2}\times 7. Rewrite the square root of the product \sqrt{500^{2}\times 7} as the product of square roots \sqrt{500^{2}}\sqrt{7}. Take the square root of 500^{2}.

$$\frac{-0.03}{\frac{\sqrt{589}}{500\sqrt{7}}}$$

Rationalize the denominator of \frac{\sqrt{589}}{500\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{-0.03}{\frac{\sqrt{589}\sqrt{7}}{500\left(\sqrt{7}\right)^{2}}}$$

The square of \sqrt{7} is 7.

$$\frac{-0.03}{\frac{\sqrt{589}\sqrt{7}}{500\times 7}}$$

To multiply \sqrt{589} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{-0.03}{\frac{\sqrt{4123}}{500\times 7}}$$

Multiply 500 and 7 to get 3500.

$$\frac{-0.03}{\frac{\sqrt{4123}}{3500}}$$

Divide -0.03 by \frac{\sqrt{4123}}{3500} by multiplying -0.03 by the reciprocal of \frac{\sqrt{4123}}{3500}.

$$\frac{-0.03\times 3500}{\sqrt{4123}}$$

Rationalize the denominator of \frac{-0.03\times 3500}{\sqrt{4123}} by multiplying numerator and denominator by \sqrt{4123}.

$$\frac{-0.03\times 3500\sqrt{4123}}{\left(\sqrt{4123}\right)^{2}}$$

The square of \sqrt{4123} is 4123.

$$\frac{-0.03\times 3500\sqrt{4123}}{4123}$$

Multiply -0.03 and 3500 to get -105.

$$\frac{-105\sqrt{4123}}{4123}$$

Divide -105\sqrt{4123} by 4123 to get -\frac{15}{589}\sqrt{4123}.

$$-\frac{15}{589}\sqrt{4123}$$