Question

In the given question, what will be the next number $83:9::146:$______

Answer 1

Step $1$: Identify the pattern :

$83$ can be written as:

$$\begin{gathered} 83=81+2 \\ \Rightarrow 83=9^2+2 \end{gathered}$$

Step $2$: Compute the required number :

Let us assume the number is $x$.

$146$ can be written as:

$$\begin{gathered} 146=x^2+2 \\ \Rightarrow x^2=146-2 \\ \Rightarrow x^2=144 \\ \Rightarrow x=\sqrt{144} \\ \Rightarrow x=12 \end{gathered}$$

Hence, the complete sequence is $83:9::146:12$.