Question

how many non perfect square numbers lie betweeen 20² and 21²
please answer this.​

Answer 1

Answer:

41

Step-by-step explanation:

Answer 2

Answer:

There are 40 non-perfect numbers between 20² and 21².

Step-by-step explanation:

Let's first generalise this and then come to the answer.

Let 'n' and '(n + 1)' be two consecutive numbers.

Then,

the Non perfect square numbers between n² and (n + 1)² will be 2n. This is purely mathematical.

We know that,

Numbers between two numbers is their difference minus 1.

For example:-

Numbers between 2 and 7 is

(7 - 2) - 1 = 4

Hence, there are 4 numbers between 2 and 7,

They are 3, 4, 5, and 6.

Now, similarly we must take the difference of their Squares,

= (((n + 1)² - n²) - 1)

= (((n² + 2n + 1²) - n²) - 1)

= ((n² + 2n + 1 - n²) - 1)

= ((2n + 1) - 1)

= (2n + 1 - 1)

= 2n

That is how we got the general formula, it is the simplified form.

Here,

n = 20 and (n + 1) = 21

So, the number of non-perfect numbers that lie between 20² and 21² = 2 × (20) = 40

Hence,

There are 40 non-perfect numbers between 20² and 21².

Hope it helped and believing you understood it........All the best