Question

Question 61

State whether the following statement is true or false:

There are 200 natural numbers between ${100}^2$ and ${101}^2$.

Answer 1

True
Natural numbers between ${100}^2$ and ${101}^2$
$={101}^2-{100}^2-1$ [$\because$ natural numbers between a and b = b - a - 1]
= (${101}^2-{100}^2$) - 1 [$a^2-b^2=(a+b)(a-b)$]
= (101 + 100) (101 - 100) - 1 = 201 - 1 = 200.