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1) = [latex] \sqrt[5]{ \frac{ a^{2}* a^{3} }{ 2^{5} } } = \sqrt[5]{ \frac{ a^{5} }{ 2^{5} } } = \frac{a}{2} [/latex] 2) = [latex] \frac{1+ \sqrt{3}(2+ \sqrt{3}) }{2+ \sqrt{3} } = \frac{1+2 \sqrt{3}+3 }{2+ \sqrt{3} } = \frac{2(2+ \sqrt{3}) }{2+ \sqrt{3} } =2[/latex] 3) = [latex] \sqrt{(37-20 \sqrt{3})(37+20 \sqrt{3}) }= \sqrt{ 37^{2}- (20 \sqrt{3}) ^{2} } = \sqrt{1369- 1200}= \sqrt{169}[/latex]=13 4) = [latex] \sqrt[7]{ \frac{ 2^{7} z^{8} }{z^4} } = \sqrt[7]{ 2^7*z^2 } = 2 \sqrt[7]{z^2}[/latex] 5) = [latex] \sqrt[24]{ 2^{36}* 3^{24}* 7^{24} }/ \sqrt{2} = 2^{ \frac{26}{24}- \frac{1}{2} } *3*7= 2^{ \frac{13}{12} } *21=42 \sqrt[12]{2} [/latex]