Given \sqrt{(224)}=(13), the value of radix r is

NIMCET 2008 Question Paper with solutions

Question : 100 of 120

Marks: +1, -0

Given

√{(224)}=(13)

, the value of radix

r

Solution:

√{(224)_{r}}=(13)_{r} ⇒ √{2 r^{2}+2 r+4}=r+3

⇒ \;\; 2 r^{2}+2 r+4=(r+3)^{2}=r^{2}+6 r+9

⇒ \;\; r^{2}-4 r-5=0

⇒ \;\; (r-5)(r+1)=0

\Rightarrow

r=-1,5

As a cannot be

-1

, so

r=5

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