Solve 13^2-{left(119/13right)}^2

$${ 13 }^{ 2 } - { \left( \frac{ 119 }{ 13 } \right) }^{ 2 }$$

Evaluate

$$\frac{14400}{169}\approx 85.207100592$$

Solution Steps

Calculate 13 to the power of 2 and get 169.

$$169-\left(\frac{119}{13}\right)^{2}$$

Calculate \frac{119}{13} to the power of 2 and get \frac{14161}{169}.

$$169-\frac{14161}{169}$$

Convert 169 to fraction \frac{28561}{169}.

$$\frac{28561}{169}-\frac{14161}{169}$$

Since \frac{28561}{169} and \frac{14161}{169} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28561-14161}{169}$$

Subtract 14161 from 28561 to get 14400.

$$\frac{14400}{169}$$

Factor

$$\frac{2 ^ {6} \cdot 3 ^ {2} \cdot 5 ^ {2}}{13 ^ {2}} = 85\frac{35}{169} = 85.20710059171597$$