Solve 68-70/frac{5.1{sqrt{50}}}

$$\frac{ 68-70 }{ \frac{ 5.1 }{ \sqrt{ 50 } } }$$

Evaluate

$$-\frac{100\sqrt{2}}{51}\approx -2.772967769$$

Solution Steps

Subtract 70 from 68 to get -2.

$$\frac{-2}{\frac{5.1}{\sqrt{50}}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{-2}{\frac{5.1}{5\sqrt{2}}}$$

Rationalize the denominator of \frac{5.1}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-2}{\frac{5.1\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{-2}{\frac{5.1\sqrt{2}}{5\times 2}}$$

Multiply 5 and 2 to get 10.

$$\frac{-2}{\frac{5.1\sqrt{2}}{10}}$$

Divide 5.1\sqrt{2} by 10 to get 0.51\sqrt{2}.

$$\frac{-2}{0.51\sqrt{2}}$$

Rationalize the denominator of \frac{-2}{0.51\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-2\sqrt{2}}{0.51\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-2\sqrt{2}}{0.51\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\sqrt{2}}{0.51}$$

Divide -\sqrt{2} by 0.51 to get -\frac{100}{51}\sqrt{2}.

$$-\frac{100}{51}\sqrt{2}$$