Solve sqrt{7^2-(7/2)^2}

$$\sqrt { 7 ^ { 2 } - ( \frac { 7 } { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{7\sqrt{3}}{2}\approx 6.062177826$$

Solution Steps

Calculate 7 to the power of 2 and get 49.

$$\sqrt{49-\left(\frac{7}{2}\right)^{2}}$$

Calculate \frac{7}{2} to the power of 2 and get \frac{49}{4}.

$$\sqrt{49-\frac{49}{4}}$$

Convert 49 to fraction \frac{196}{4}.

$$\sqrt{\frac{196}{4}-\frac{49}{4}}$$

Since \frac{196}{4} and \frac{49}{4} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{196-49}{4}}$$

Subtract 49 from 196 to get 147.

$$\sqrt{\frac{147}{4}}$$

Rewrite the square root of the division \sqrt{\frac{147}{4}} as the division of square roots \frac{\sqrt{147}}{\sqrt{4}}.

$$\frac{\sqrt{147}}{\sqrt{4}}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$\frac{7\sqrt{3}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{7\sqrt{3}}{2}$$