Final answer:
To rationalize the expression (4 - √5)(4 √5)/(2 √11) in the form √(a/b)×√11 where a and b are integers, first simplify the numerator using the difference of squares formula. Then, rewrite the expression with the simplified numerator. Finally, rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.
Step-by-step explanation:
To write the expression (4 - √5)(4 √5)/(2 √11) in the form of √(a/b) √11, where a and b are integers, we need to rationalize the denominator. First, let's simplify the numerator by using the difference of squares formula:
(4 - √5)(4 √5) = 16 - 4√5 + 4√5 - 5 = 16 - 5 = 11
Now, let's rewrite the expression with the simplified numerator:
11/(2 √11)
To rationalize the denominator, multiply both the numerator and the denominator by the conjugate of the denominator:
(11/(2 √11)) * (√11/(√11)) = (11√11)/(2 √(11^2)) = (11√11)/(2 √121) = (11√11)/22
Therefore, the expression (4 - √5)(4 √5)/(2 √11) can be written as (11√11)/22.