Solve 13000-12500/sqrt{16250-15625sqrt{10900-10000}}

$$\frac { 13000 - 12500 } { \sqrt { 16250 - 15625 } \sqrt { 10900 - 10000 } }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Subtract 12500 from 13000 to get 500.

$$\frac{500}{\sqrt{16250-15625}\sqrt{10900-10000}}$$

Subtract 15625 from 16250 to get 625.

$$\frac{500}{\sqrt{625}\sqrt{10900-10000}}$$

Calculate the square root of 625 and get 25.

$$\frac{500}{25\sqrt{10900-10000}}$$

Subtract 10000 from 10900 to get 900.

$$\frac{500}{25\sqrt{900}}$$

Calculate the square root of 900 and get 30.

$$\frac{500}{25\times 30}$$

Multiply 25 and 30 to get 750.

$$\frac{500}{750}$$

Reduce the fraction \frac{500}{750} to lowest terms by extracting and canceling out 250.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$