Question

how many integer number between 3^3 and 4^3 ,where ^ is power​

Answer 1

Answer:

There are 36 numbers between 3³ and 4³

Step-by-step explanation:

First we must know what 'between' here means.

Numbers between two integers is exclusive of the integers itself.

For ex:-

Numbers between 3 and 8 = 4, 5, 6, 7

See 3 and 8 is not included in the list

Also,

Number of integers between two integers a and b, where a > b = (a - b) - 1

For ex:- Numbers between 3 and 8 is,

(8 - 3) - 1 = 5 - 1 = 4

So, there are 4 numbers between 3 and 8

They are 4, 5, 6, 7.

Now,

We must find the integers between 3³ and 4³.

Now,

3³ = 27

4³ = 64

So,

The numbers between 64 and 27 = (64 - 27) - 1

= 37 - 1

= 36

Hence,

There are 36 numbers between 3³ and 4³

Now,

we can form a generalised formula for this purpose.

We know that, where a > b

a³ - b³ = (a - b)(a² + ab + b²)

Now,

For the number between a³ and b³

(a³ - b³) - 1 = [(a - b)(a² + ab + b²)] - 1

So,

The general formula is = [(a - b)(a² + ab + b²)] - 1

Brackets are just used to that you know what to do first.

Now, you might feel that this is unnecessary, but the truth is its not.

Here, We got a small number such as 3 and 4, but if they ask us about 32³ and 54³, its is pretty hard to calculate it in less time, that is where our general formula plays an important role.

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