Solve sqrt{13^2-(19/2)^2}

$$\sqrt { 13 ^ { 2 } - ( \frac { 19 } { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{3\sqrt{35}}{2}\approx 8.874119675$$

Solution Steps

Calculate 13 to the power of 2 and get 169.

$$\sqrt{169-\left(\frac{19}{2}\right)^{2}}$$

Calculate \frac{19}{2} to the power of 2 and get \frac{361}{4}.

$$\sqrt{169-\frac{361}{4}}$$

Convert 169 to fraction \frac{676}{4}.

$$\sqrt{\frac{676}{4}-\frac{361}{4}}$$

Since \frac{676}{4} and \frac{361}{4} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{676-361}{4}}$$

Subtract 361 from 676 to get 315.

$$\sqrt{\frac{315}{4}}$$

Rewrite the square root of the division \sqrt{\frac{315}{4}} as the division of square roots \frac{\sqrt{315}}{\sqrt{4}}.

$$\frac{\sqrt{315}}{\sqrt{4}}$$

Factor 315=3^{2}\times 35. Rewrite the square root of the product \sqrt{3^{2}\times 35} as the product of square roots \sqrt{3^{2}}\sqrt{35}. Take the square root of 3^{2}.

$$\frac{3\sqrt{35}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{3\sqrt{35}}{2}$$