Solve 68-70/frac{51{sqrt{50}}}

$$\frac{ 68-70 }{ \frac{ 51 }{ \sqrt{ 50 } } }$$

Evaluate

$$-\frac{10\sqrt{2}}{51}\approx -0.277296777$$

Solution Steps

Subtract 70 from 68 to get -2.

$$\frac{-2}{\frac{51}{\sqrt{50}}}$$

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}.

$$\frac{-2}{\frac{51}{5\sqrt{2}}}$$

Rationalize the denominator of \frac{51}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-2}{\frac{51\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{-2}{\frac{51\sqrt{2}}{5\times 2}}$$

Multiply 5 and 2 to get 10.

$$\frac{-2}{\frac{51\sqrt{2}}{10}}$$

Divide -2 by \frac{51\sqrt{2}}{10} by multiplying -2 by the reciprocal of \frac{51\sqrt{2}}{10}.

$$\frac{-2\times 10}{51\sqrt{2}}$$

Rationalize the denominator of \frac{-2\times 10}{51\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-2\times 10\sqrt{2}}{51\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-2\times 10\sqrt{2}}{51\times 2}$$

Multiply -2 and 10 to get -20.

$$\frac{-20\sqrt{2}}{51\times 2}$$

Multiply 51 and 2 to get 102.

$$\frac{-20\sqrt{2}}{102}$$

Divide -20\sqrt{2} by 102 to get -\frac{10}{51}\sqrt{2}.

$$-\frac{10}{51}\sqrt{2}$$