Question

Find the radix of the scale in which $554$ represents the square of $24$.

Answer 1

$(\sqrt{554}{)}_b=(24{)}_b$

$\Rightarrow \sqrt{4\times b^0+5\times b^1+5\times b^2}=4\times b^0+2\times b^1$

$\Rightarrow 4+5b+5b^2=(2b+4{)}^2$

$\Rightarrow 4+5b+5b^2=4b^2+16+16b$

$\Rightarrow b^2-11b-12=0$

$\Rightarrow b=12$