This question asked in GATE 1997
subject: Electronics
Q6. Given √(224)r= (13)r
The value of the radix r is:
(a) 10 (b) 8 (c) 5 (d) 6
ANSWER:
Firstly , what is given in the question
√(224)r= (13)r
Squaring both sides
Above equation can be written as: (224)r = ((13)r)^2
Step 1:
Converting to decimal number:
Left side of the equation:
4 will multiply by r^0 , 2 will multilpy by r^1 and 2 will multiply by r^2 i.e 2r^2 + 2r^1 + 4r^0
Right side of the equation
3 will multiply by r^0 and 1 will multiply by r^1 i.e (1r^1 + 3r^0)2
Step 2:
Now, LHS = RHS
2r^2 + 2r + 4 = (r + 3)^2 ( because any number with exponential value 0 consider as 1)
r^2 – 4r – 5 = 0 ( apply formaula ( a + b) ^2 where a is r and b is 3)
Root of the above equation is 5, -1.
Therefore radix = 5