Solve frac{sqrt{59.29}-sqrt{5.29}}{sqrt{59.29}+sqrt{5.29}}

$$\frac { \sqrt { 59.29 } - \sqrt { 5.29 } } { \sqrt { 59.29 } + \sqrt { 5.29 } }$$

Evaluate

$$0.54$$

Solution Steps

Calculate the square root of 59.29 and get 7.7.

$$\frac{7.7-\sqrt{5.29}}{\sqrt{59.29}+\sqrt{5.29}}$$

Calculate the square root of 5.29 and get 2.3.

$$\frac{7.7-2.3}{\sqrt{59.29}+\sqrt{5.29}}$$

Subtract 2.3 from 7.7 to get 5.4.

$$\frac{5.4}{\sqrt{59.29}+\sqrt{5.29}}$$

Calculate the square root of 59.29 and get 7.7.

$$\frac{5.4}{7.7+\sqrt{5.29}}$$

Calculate the square root of 5.29 and get 2.3.

$$\frac{5.4}{7.7+2.3}$$

Add 7.7 and 2.3 to get 10.

$$\frac{5.4}{10}$$

Expand \frac{5.4}{10} by multiplying both numerator and the denominator by 10.

$$\frac{54}{100}$$

Reduce the fraction \frac{54}{100} to lowest terms by extracting and canceling out 2.

$$\frac{27}{50}$$

Factor

$$\frac{3 ^ {3}}{2 \cdot 5 ^ {2}} = 0.54$$