Solve 37.5-(1.649)(2.95)/sqrt{90}

$$37.5 - \frac { ( 1.649 ) ( 2.95 ) } { \sqrt { 90 } }$$

Evaluate

$$-\frac{97291\sqrt{10}}{600000}+37.5\approx 36.987231407$$

Solution Steps

Multiply 1.649 and 2.95 to get 4.86455.

$$37.5-\frac{4.86455}{\sqrt{90}}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$37.5-\frac{4.86455}{3\sqrt{10}}$$

Rationalize the denominator of \frac{4.86455}{3\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$37.5-\frac{4.86455\sqrt{10}}{3\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$37.5-\frac{4.86455\sqrt{10}}{3\times 10}$$

Multiply 3 and 10 to get 30.

$$37.5-\frac{4.86455\sqrt{10}}{30}$$

Divide 4.86455\sqrt{10} by 30 to get \frac{97291}{600000}\sqrt{10}.

$$37.5-\frac{97291}{600000}\sqrt{10}$$