Question

Fill in the blank

$\begin{array}{ccc}25& 12& 49\\ 81& 13& 16\\ 36& 14& ....\end{array}$

Answer 1

Observe the numbers in each row. The middle number in each row is the sum of the square roots of the first number and the last number.
$\sqrt{a}+\sqrt{c}=b$
The same relation can be written in the following form also.
$(b-\sqrt{a}{)}^2=c$
$(12-\sqrt{25}{)}^2=(12-5{)}^2=7^2=49$
$(13-\sqrt{81}{)}^2=(13-9{)}^2=4^2=16$
Thus, the missing number is: $(14-\sqrt{36}{)}^2=(14-6{)}^2=8^2=64$