There are _________ natural numbers between n² and (n + 1)². Fill in the blanks to make the statement true.

Solution:

Given, there are ________ natural numbers between n² and (n+1)².

We have to fill in the blanks to make the statement true.

Natural numbers between n² and (n+1)² = [(n+1)² - n²] - 1

By using algebraic identity,

(a+b)² = a² + 2ab + b²

So, (n+1)² = n² + 2n + 1

Now, [(n+1)² - n²] - 1 = n² + 2n + 1 - n² - 1

= 2n

Therefore, the natural numbers between n² and (n+1)² is 2n.

✦ Try This: There are _________ natural numbers between 10² and 11². Fill in the blanks to make the statement true.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 3 Problem 29

There are _________ natural numbers between n² and (n + 1)². Fill in the blanks to make the statement true

Summary:

There are 2n natural numbers between n² and (n + 1)².

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