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If \(554_b\) is the base b representation of the square of the number whose base b representation is \(24_b\) then find b.

 Jan 5, 2019
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\(554_b = (24_b)^2\\ 5b^2+5b+4 = (2b+4)^2 = 4b^2+16b+16\\ b^2- 11b-12=0\\ (b-12)(b+1) = 0\\ b=12,~-1\\ \text{-1 is not a base}\\ b=12\)

 

\(554 _{12} = 4+60+720 = 784_d\\ 24_{12}=24+4=28_d\\ 748=28^2\)

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 Jan 5, 2019

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