Question

How many natural numbers lie between the squares of 21 and 22 ?

Answer 1

Answer:

The number of natural numbers lying between the squares of 21 and 22 is 42.

Step-by-step explanation:

Given: the square of the numbers 21 and 22.

(21)^2=441

(22)^2=484

To Find: Number of natural numbers lying between the squares of 21 and 22.

Solution:      

(1) We know that numbers whose squares end with the digit 2,3,7,8 and an odd number of zeroes are called non-perfect numbers.

(2) It is to be noted that the number of natural numbers between squares of any two consecutive non-perfect numbers is 2n, when n denotes the first number and so the next number is (n+1).

Observing the above-mentioned two points we can understand that 21 and 22 are non-perfect numbers.

Also, in this case, n=21 and n+1=22

Therefore, from the formula, we see that the number of natural numbers lying between (22)^2 and (21)^2 are 2n or 2x21 = 42.

Hence, the number of natural numbers lying between the squares of 21 and 22 is 42.

Answer 2

42 Natural numbers lie between the squares of 21 and 22.

Given numbers: 21 and 22

The Square of the numbers is :

$21^{2}$  =441

$22^{2}$ =484

What to Find: The total number of natural numbers lying between the squares of 21 and 22.

• We know that the numbers in which the squares end with the digit 2,3,7,8 and an odd number of zeroes are called non-perfect numbers.

• It is noted that the number of natural numbers between squares of  two consecutive non-perfect numbers is 2n,
• Here,  n denotes the first number and so the next number is (n+1).

• From the observation of the above mentioned 2 points we can understand that 21 & 22 are non-perfect numbers.

• In the case of this question, n=21 and n+1=22

• Hereby, from the formula above we can see that the number of natural numbers lying between $21^{2}$ and $22^{2}$ are :

        2n or 2x21 = 42.

• Therefore the total number of natural numbers lie in between the squares of 21 & 22 is 42.