Question

Q2. Which of the following is the number non-perfect square numbers' between the square of the numbers n and n+1? (i) n+1 (ii) n (iii) 2n (iv) 2n+1​

Answer 1

Given: Two numbers n^2 and (n+1)^2

To find: Which is the number non-perfect square numbers between two given numbers?

Solution:

• Now we know that we we have given two consecutive numbers, that is n and n+1.

• So lets consider some cases.

             Case 1: n = 1 and n+1 = 2

             n^2 = 1 and (n+1)^2 = 4

• So there are two numbers in between square of 1 and 2.

             Case 2: n = 4 and n+1 = 5

             n^2 = 16 and (n+1)^2 = 25

• So total numbers between the square of 4 and 5 are 8.

• So from case 1 and case 2 we can see that there are twice of first number as elements in between two consecutive squared numbers, that is 2(1) in first case and 2(4) in second case.

Answer:

               So we can say that there are 2n non-perfect square numbers between two given numbers.

Answer 2

Answer:

2n

Step-by-step explanation:

In The ScreenShot Below~

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