Solve sqrt{{left(119/26right)}^2+{left(60/13right)}^2}

$$\sqrt{ { \left( \frac{ 119 }{ 26 } \right) }^{ 2 } + { \left( \frac{ 60 }{ 13 } \right) }^{ 2 } }$$

Evaluate

$$\frac{13}{2}=6.5$$

Solution Steps

Calculate \frac{119}{26} to the power of 2 and get \frac{14161}{676}.

$$\sqrt{\frac{14161}{676}+\left(\frac{60}{13}\right)^{2}}$$

Calculate \frac{60}{13} to the power of 2 and get \frac{3600}{169}.

$$\sqrt{\frac{14161}{676}+\frac{3600}{169}}$$

Least common multiple of 676 and 169 is 676. Convert \frac{14161}{676} and \frac{3600}{169} to fractions with denominator 676.

$$\sqrt{\frac{14161}{676}+\frac{14400}{676}}$$

Since \frac{14161}{676} and \frac{14400}{676} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{14161+14400}{676}}$$

Add 14161 and 14400 to get 28561.

$$\sqrt{\frac{28561}{676}}$$

Reduce the fraction \frac{28561}{676} to lowest terms by extracting and canceling out 169.

$$\sqrt{\frac{169}{4}}$$

Rewrite the square root of the division \frac{169}{4} as the division of square roots \frac{\sqrt{169}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{13}{2}$$

Factor

$$\frac{13}{2} = 6\frac{1}{2} = 6.5$$