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\sqrt{1^{2}+\left(-\frac{2}{3}+\frac{3}{2}\right)^{2}}
Add -1 and 2 to get 1.
\sqrt{1+\left(-\frac{2}{3}+\frac{3}{2}\right)^{2}}
Calculate 1 to the power of 2 and get 1.
\sqrt{1+\left(\frac{5}{6}\right)^{2}}
Add -\frac{2}{3} and \frac{3}{2} to get \frac{5}{6}.
\sqrt{1+\frac{25}{36}}
Calculate \frac{5}{6} to the power of 2 and get \frac{25}{36}.
\sqrt{\frac{61}{36}}
Add 1 and \frac{25}{36} to get \frac{61}{36}.
\frac{\sqrt{61}}{\sqrt{36}}
Rewrite the square root of the division \sqrt{\frac{61}{36}} as the division of square roots \frac{\sqrt{61}}{\sqrt{36}}.
\frac{\sqrt{61}}{6}
Calculate the square root of 36 and get 6.