There are 200 natural numbers between 100² and 101². State whether the statement is true or false.

Solution:

Given, there are 200 natural numbers between 100² and 101².

We have to determine if the given statement is true or false.

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

= n² + 2n + 1 - n² - 1

= 2n

Natural numbers between n² and (n+1)² is 2n.

Here, n = 100

n+1 = 101

Natural numbers between 100² and 101² = 2(100)

= 200

Therefore, there are 200 natural numbers between 100² and 101².

✦ Try This: There are 20 natural numbers between 10² and 11². State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 8 Maths

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NCERT Exemplar Class 8 Maths Chapter 3 Problem 61

There are 200 natural numbers between 100² and 101². State whether the statement is true or false

Summary:

The given statement, ”There are 200 natural numbers between 100² and 101²” is true.

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