Solve sqrt{200/2.25*20000+9.5*14000}

$$\sqrt{ \frac{ 200 }{ 2.25 \times 20000+9.5 \times 14000 } }$$

Evaluate

$$\frac{\sqrt{890}}{890}\approx 0.033520076$$

Solution Steps

Multiply 2.25 and 20000 to get 45000.

$$\sqrt{\frac{200}{45000+9.5\times 14000}}$$

Multiply 9.5 and 14000 to get 133000.

$$\sqrt{\frac{200}{45000+133000}}$$

Add 45000 and 133000 to get 178000.

$$\sqrt{\frac{200}{178000}}$$

Reduce the fraction \frac{200}{178000} to lowest terms by extracting and canceling out 200.

$$\sqrt{\frac{1}{890}}$$

Rewrite the square root of the division \sqrt{\frac{1}{890}} as the division of square roots \frac{\sqrt{1}}{\sqrt{890}}.

$$\frac{\sqrt{1}}{\sqrt{890}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{890}}$$

Rationalize the denominator of \frac{1}{\sqrt{890}} by multiplying numerator and denominator by \sqrt{890}.

$$\frac{\sqrt{890}}{\left(\sqrt{890}\right)^{2}}$$

The square of \sqrt{890} is 890.

$$\frac{\sqrt{890}}{890}$$