Whats the method to find the base of any given number,
eg. (121) r = (144) 8
here r and 8 is a base
So how do i find the value of r?
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By definition $$144_8=1\cdot8^2+4\cdot8^1+4\cdot8^0=64+32+4=100\;,$$ and $$121_r=1\cdot r^2+2\cdot r^1+1\cdot r^0=r^2+2r+1\;.$$ To find $r$, just solve the quadratic equation $$r^2+2r+1=100$$ by whatever method you find most convenient; the slickest method is probably to notice that $r^2+2r+1=(r+1)^2$, so $(r+1)^2=100=10^2$. |
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