Solve 2500*frac{sqrt{145}}{50}+frac{14400/1/100sqrt{145}}{50}

$$2500 \times \frac{ \sqrt{ 145 } }{ 50 } + \frac{ \frac{ \frac{ 14400 }{ 1 } }{ 100 \sqrt{ 145 } } }{ 50 }$$

Evaluate

$$\frac{181322\sqrt{145}}{3625}\approx 602.318899922$$

Solution Steps

Cancel out 50, the greatest common factor in 2500 and 50.

$$50\sqrt{145}+\frac{\frac{\frac{14400}{1}}{100\sqrt{145}}}{50}$$

Express \frac{\frac{\frac{14400}{1}}{100\sqrt{145}}}{50} as a single fraction.

$$50\sqrt{145}+\frac{\frac{14400}{1}}{100\sqrt{145}\times 50}$$

Anything divided by one gives itself.

$$50\sqrt{145}+\frac{14400}{100\sqrt{145}\times 50}$$

Multiply 100 and 50 to get 5000.

$$50\sqrt{145}+\frac{14400}{5000\sqrt{145}}$$

Rationalize the denominator of \frac{14400}{5000\sqrt{145}} by multiplying numerator and denominator by \sqrt{145}.

$$50\sqrt{145}+\frac{14400\sqrt{145}}{5000\left(\sqrt{145}\right)^{2}}$$

The square of \sqrt{145} is 145.

$$50\sqrt{145}+\frac{14400\sqrt{145}}{5000\times 145}$$

Cancel out 200 in both numerator and denominator.

$$50\sqrt{145}+\frac{72\sqrt{145}}{25\times 145}$$

Multiply 25 and 145 to get 3625.

$$50\sqrt{145}+\frac{72\sqrt{145}}{3625}$$

Combine 50\sqrt{145} and \frac{72\sqrt{145}}{3625} to get \frac{181322}{3625}\sqrt{145}.

$$\frac{181322}{3625}\sqrt{145}$$