isro cs question paper solution 2018 Q19 Set-A

Given √224_r = 13_r  the value of radix r is

(a) 10
(b) 8
(c) 6
(d) 5

Correct answer is:  (d) 5

for radix r =10,  13 is not the root of 224
for radix r =8,  224r = (64*2+8*2+4) =128+20 =148 is not a perfect square
for radix r =6,  224r = (36*2+6*2+4) =72+16 =88 is not a perfect square
for radix r =5, 224r = (25*2+5*2+4) =50+14 =64 is a perfect square.So, square root of 64 =8 =(13)₅