Product of Two Consecutive Even or Odd Natural Numbers

Q. How many numbers lie between the squares of the numbers $99$ and $100$?
[2 marks]

1. $200$
2. $199$
3. $201$
4. $198$

Q.

find the following product 43x45?

1. 1835

2. 1935

3. 2115

4. 2025

Q. If the product of four consecutive natural numbers increased by a natural number $\rho$ is a perfect square, then the value of $\rho$ is:

1. 4
2. 2
3. 8
4. 1

Q.

find the following product 43x45?

1. 1935

2. 1835

3. 2115

4. 2025

Q.

Evaluate: $\left(i\right)69\times 71$, (ii) $94\times 106$.

Q.

Observe the following pattern:

$2^2-1^2=2+13^2-2^2=3+24^2-3^2=4+35^2-4^2=5+4$

Find the value of
(i) ${100}^2-{99}^2$ (ii) ${111}^2-{109}^2$
(iii) ${99}^2-{96}^2$

Q. Evaluate: (i) $88\times 92$, (ii) $78\times 82$.

Q. Find the least number which must be added to the following number to make it perfect square:
$4931$

Q. $(96{)}^2-1$ is a product of two consecutive odd numbers. Find those two odd numbers.

1. 96 and 98
2. 93 and 95
3. 95 and 97
4. 99 and 101

Q. State whether the following statement is true or false
The sum of two odd numbers is an odd number.

1. True
2. False