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Given $\sqrt{(224)_r} =(13)_r$.

The value of the radix $r$ is:

1. $10$
2. $8$
3. $5$
4. $6$
edited | 1.7k views

$\sqrt{}$(224)r = (13)r

convert r base to decimal

$\sqrt{}$2r2 + 2r + 4 = r + 3

take square both sides

2r2 + 2r + 4 = r2 + 6r+ 9

r2 - 4r -5 = 0

r2 -5r +r - 5 = 0

(r-5)(r+1)=0

r can not be -1 so

r = 5 is correct answer

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In such type of question s always  convert unknown  base  given  i.e base  b,  to decimal  i.e base 10  and  perform operations  simple concept  so answer is 5

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