Question

Which of the following is the non-perfect square numbers’ between the square of the numbers n and n + 1?
n+1
n
2n
2n+1​

pls answer correctly

Answer 1

Answer:

2n

Step-by-step explanation:

If n is a whole number then its square will n²

If n + 1 is the next number then the square will be (n + 1)² = n² + 2×n×1 + 1² = n² + 2n + 1

So Difference of two squares are

(n + 1)² - n² = (n² + 2n + 1) - n² = n² + 2n + 1 - n² = 2n + 1

so to get the next square we just need to add 2n + 1 to n²

Let's check the result

Let the numbers be 5 and 6

n² = 5² = 25

(n + 1)² = 6² = 36

By our result,

6² - 5² = 36 - 25 = 11 = 2(5) + 1

so it is right,

Hence there are 2n non perfect square numbers between 2 square numbers.

let's choose the numbers 1 and 2

n² = 1² = 1

(n + 1)² = 2² = 4

Numbers between n² and (n + 1)² here is 2 and 3 that so there are two numbers

2n = 2 × 1 = 2 numbers

we check it with any two consecutive numbers

3² = 9

4² = 16

so numbers between = 10, 11, 12, 13, 14, 15

so number of numbers between = 6 = 2n = 2 × 3

Hope you understood it........All the best