How many natural numbers between (n)square and (n+1)square.
Please show the formulae also.
Answers
Given:
First value = n
Second value = (n+1)
To find:
Total natural numbers between (n)² and (n+1)² =?
Solution:
- We know that n² and (n+1)² are consecutive squares therefore the natural numbers between them are not a perfect square.
- Subtract the smaller square from the greater square number.
- To find the natural numbers between squares of two given numbers the steps are as follows:
- (n)² = smaller square
- (n+1)²= greater square
∴ Natural numbers between two consecutive squares = (n+1)² - (n)² - 1
= (n² + 2n + 1) - n² - 1 [∵(a+b)² = a² + 2ab + b²]
= 2n
Hence, 2n natural numbers are present between n² and (n+1)².
First value =n
Second value =(n+1)
To find:
Total natural numbers between (n) ^ 2 and (n + 1) ^ 2 =7
Solution:
We know that n ^ 2 and (n + 1) ^ 2 are consecutive squares therefore the natural numbers between them are not a perfect square.
Subtract the smaller square from the greater square number.
To find the natural numbers between squares of two given numbers the steps are as follows:
⚫ (n) ^ 2 = smaller square
• (n + 1) ^ 2 = greater square
.. Natural numbers between two consecutive squares =(n+1)^ 2 -(n)^ 2 -1
b^ 2 ]
=(n^ 2 +2n+1)-n^ 2 -1[:(a+b)^ 2 =a^ 2 +2ab+
=2n
Here this help you