Solve 225.9-230/10/sqrt{34}

$$\frac{ \frac{ 225.9-230 }{ 10 } }{ \sqrt{ 34 } }$$

Evaluate

$$-\frac{41\sqrt{34}}{3400}\approx -0.07031442$$

Solution Steps

Express \frac{\frac{225.9-230}{10}}{\sqrt{34}} as a single fraction.

$$\frac{225.9-230}{10\sqrt{34}}$$

Subtract 230 from 225.9 to get -4.1.

$$\frac{-4.1}{10\sqrt{34}}$$

Rationalize the denominator of \frac{-4.1}{10\sqrt{34}} by multiplying numerator and denominator by \sqrt{34}.

$$\frac{-4.1\sqrt{34}}{10\left(\sqrt{34}\right)^{2}}$$

The square of \sqrt{34} is 34.

$$\frac{-4.1\sqrt{34}}{10\times 34}$$

Multiply 10 and 34 to get 340.

$$\frac{-4.1\sqrt{34}}{340}$$

Divide -4.1\sqrt{34} by 340 to get -\frac{41}{3400}\sqrt{34}.

$$-\frac{41}{3400}\sqrt{34}$$