Answer:
3.3164 correct to four decimal places
Step-by-step explanation:
WE USE BINOMIAL THEOREM.
√11=√(10+1)=(10 + 1)^½
FACTOR TEN OUT
=> 10^½(1 +1/10)^½
WE KNOW THAT:
(1 +X) ^n= 1 + nX + [n(n -1)(x)²]/2! + .........
NOW LET X =1/10 AND n= ½
SUBSTITUTING INTO THE FORMULA ABOVE
=>(1/10)^½ [1 + (½)(1/10) +[½(½ –1)(1/10)^½]/2×1 + ......]
=(1/10)^½[1 + 1/20–1/800 +......]
=> (1/10)^½(839/800)
≈3.3164
THEREFORE √11 ≈ 3.3164( ESTIMATED)
