Solve 57-75/sqrt{126*35}

$$\frac { 57 - 75 } { \sqrt { 126 \times 35 } }$$

Evaluate

$$-\frac{3\sqrt{10}}{35}\approx -0.271052371$$

Solution Steps

Subtract 75 from 57 to get -18.

$$\frac{-18}{\sqrt{126\times 35}}$$

Multiply 126 and 35 to get 4410.

$$\frac{-18}{\sqrt{4410}}$$

Factor 4410=21^{2}\times 10. Rewrite the square root of the product \sqrt{21^{2}\times 10} as the product of square roots \sqrt{21^{2}}\sqrt{10}. Take the square root of 21^{2}.

$$\frac{-18}{21\sqrt{10}}$$

Rationalize the denominator of \frac{-18}{21\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{-18\sqrt{10}}{21\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{-18\sqrt{10}}{21\times 10}$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{-3\sqrt{10}}{5\times 7}$$

Multiply 5 and 7 to get 35.

$$\frac{-3\sqrt{10}}{35}$$