Select the missing number from the given responses.
64 36 2
81 25 4
144 16 ?
(a) 6
(b) 8
(c) 3
(d) 16

Hint: To solve this question first we will try to figure out which pattern is followed by elements of first row and then we will verify the same pattern in row second. After verification, we will let the missing number be x, and then we will apply a pattern in the last row, to evaluate the value of x.

Complete step-by-step answer:
Now, in question we are given two solved rows and we have to find the last digit of the third row, which is the last row.
In question, in which we have to find the missing number, all are bound with the same pattern which helps in evaluating the missing number using that hint.
So, now firstly we see what the pattern is in the first row.
In the first row, we have the first element as 64, then second element as 36 and last element is 2.
So, if we see carefully if we take square root of 64 and square root of 36 and the, if we subtract square root of 36 from square root of 64, we will have number 2.
That is, \[\sqrt{64}=8\] and \[\sqrt{36}=6\], and
\[\sqrt{64}-\sqrt{36}=8-6\]
\[\sqrt{64}-\sqrt{36}=2\]
Now, let us check whether this pattern is applicable in the second row.
In the first row, we have the first element as 81, then second element as 25 and last element is 4.
So, \[\sqrt{81}=9\] and \[\sqrt{25}=5\], and
\[\sqrt{81}-\sqrt{25}=9-5\]
\[\sqrt{81}-\sqrt{25}=4\]
So, both the first and second row have the same pattern among all three elements, which is the difference between the first two elements of a row and the third element of the row.
So, in the third row we have the first element as 144, then second element as 16 and let last element is x.
So, \[\sqrt{144}=12\] and \[\sqrt{16}=4\], and
\[\sqrt{144}-\sqrt{16}=12-4\]
\[\sqrt{144}-\sqrt{16}=8\]
So, according to pattern followed by first, second and third row, last element of third row is x = 8

So, the correct answer is “Option (b)”.

Note: To solve such a question, one must think and try all possible ways to find out the pattern which can be fit in each row. The calculation of each row must be done properly as this can change the values of the last element of the third row and even change the original pattern of the question.