Solve sqrt{(-1/2-6)^2+(11/2-1)^2}

$$\sqrt { ( - \frac { 1 } { 2 } - 6 ) ^ { 2 } + ( \frac { 11 } { 2 } - 1 ) ^ { 2 } }$$

Evaluate

$$\frac{5\sqrt{10}}{2}\approx 7.90569415$$

Solution Steps

Subtract 6 from -\frac{1}{2} to get -\frac{13}{2}.

$$\sqrt{\left(-\frac{13}{2}\right)^{2}+\left(\frac{11}{2}-1\right)^{2}}$$

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

$$\sqrt{\frac{169}{4}+\left(\frac{11}{2}-1\right)^{2}}$$

Subtract 1 from \frac{11}{2} to get \frac{9}{2}.

$$\sqrt{\frac{169}{4}+\left(\frac{9}{2}\right)^{2}}$$

Calculate \frac{9}{2} to the power of 2 and get \frac{81}{4}.

$$\sqrt{\frac{169}{4}+\frac{81}{4}}$$

Add \frac{169}{4} and \frac{81}{4} to get \frac{125}{2}.

$$\sqrt{\frac{125}{2}}$$

Rewrite the square root of the division \sqrt{\frac{125}{2}} as the division of square roots \frac{\sqrt{125}}{\sqrt{2}}.

$$\frac{\sqrt{125}}{\sqrt{2}}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

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

Rationalize the denominator of \frac{5\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{5\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{5\sqrt{10}}{2}$$