If \(554_b\) is the base b representation of the square of the number whose base b representation is \(24_b\) then find b.
\(554_b = (24_b)^2\\ 5b^2+5b+4 = (2b+4)^2 = 4b^2+16b+16\\ b^2- 11b-12=0\\ (b-12)(b+1) = 0\\ b=12,~-1\\ \text{-1 is not a base}\\ b=12\)
\(554 _{12} = 4+60+720 = 784_d\\ 24_{12}=24+4=28_d\\ 748=28^2\)
+537 
