Question

Match the following.

• A. 1110
• B. 42
• C. 2×3
• D. 2×5

Answer 1

Between $n^2$ and $(n+1{)}^2$, there are $2n$ non-square natural numbers.
$\therefore$ Between $3^2$ and $4^2$, there are $2\times 3=6$ non-square natural numbers.

Similarly, between $5^2$ and $6^2$, there are $2\times 5=10$ non-square natural numbers.

Sum of first $n$ odd natural numbers will be equal to $n^2$.
$\therefore$ 1 + 3 + 5 + 7 = $4^2$ = 16

111 + 999 = 111 + (1000 - 1)
= (111 + 1000) - 1
= 1111 - 1
= 1110