Solve sqrt{({left(13/2right)}^2-36}

$$\sqrt{ ( { \left( \frac{ 13 }{ 2 } \right) }^{ 2 } -36 }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Calculate \frac{13}{2} to the power of 2 and get \frac{169}{4}.

$$\sqrt{\frac{169}{4}-36}$$

Convert 36 to fraction \frac{144}{4}.

$$\sqrt{\frac{169}{4}-\frac{144}{4}}$$

Since \frac{169}{4} and \frac{144}{4} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{169-144}{4}}$$

Subtract 144 from 169 to get 25.

$$\sqrt{\frac{25}{4}}$$

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$