Question

How many non square numbers lie between 80 square and 81 square?

Answer 1

Answer:

8 non square numbers lie between 80 square and 81 square.

Step-by-step explanation:

Answer 2

The number of non-square numbers lie between 80 square and 81 square is 160

Given :

The number 80 square and 81 square

To find :

The number of non-square numbers lie between 80 square and 81 square

Concept :

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

Solution :

Step 1 of 2 :

Here the given numbers are 80² and 81²

80² = 6400

81² = 6561

The natural numbers lie between 80 square and 81 square are 6401 , 6402 , 6403 , ... , 6560

This is an arithmetic progression

Step 2 of 2 :

Find the number of term

The numbers are 6401 , 6402 , 6403 , ... , 6560

First term = a = 6401

Common Difference = d = 6402 - 6401 = 1

Let 6560 is the nth term of the AP

⇒ a + ( n - 1 )d = 6560

⇒ 6401 + ( n - 1 ) = 6560

⇒ n + 6400 = 6560

⇒ n = 6560 - 6400

⇒ n = 160

The number of non-square numbers lie between 80 square and 81 square is 160

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