Answer
$\left( \cos \dfrac {\pi }{4}+\sin \dfrac {\pi }{6}\right) ^{2}=\dfrac {3+2\sqrt {2}}{4}\approx 1.457$
Work Step by Step
$\left( \cos \dfrac {\pi }{4}+\sin \dfrac {\pi }{6}\right) ^{2}=\left( \dfrac {\sqrt {2}}{2}+\dfrac {1}{2}\right) ^{2}=\dfrac {\left( \sqrt {2}\right) ^{2}+1^{2}+2\times 1\times \sqrt {2}}{4}=\dfrac {3+2\sqrt {2}}{4}\approx 1.457$