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q-2-2-2-




Question Number 159839 by abelpedro last updated on 21/Nov/21
q=2(√(2(√2)))
$${q}=\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}}} \\ $$
Answered by abdullah_ff last updated on 21/Nov/21
q = 2(√(2(√2)))  = 2(√(2^1 ∙2^(1/2) ))  = 2(√2^(1+(1/2)) )  = 2(√2^(3/2) )  = 2^1 ∙2^(3/4)   = 2^(7/4)
$${q}\:=\:\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}}} \\ $$$$=\:\mathrm{2}\sqrt{\mathrm{2}^{\mathrm{1}} \centerdot\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{2}}} } \\ $$$$=\:\mathrm{2}\sqrt{\mathrm{2}^{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}} } \\ $$$$=\:\mathrm{2}\sqrt{\mathrm{2}^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$$$=\:\mathrm{2}^{\mathrm{1}} \centerdot\mathrm{2}^{\frac{\mathrm{3}}{\mathrm{4}}} \\ $$$$=\:\mathrm{2}^{\frac{\mathrm{7}}{\mathrm{4}}} \\ $$

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