Question

How many non square number lie between the following pair of number?
(c) 80 square and 81 square​

Answer 1

Answer:

80 square =6400

81 square =6561

diff =6561-6400=161

so there r 161 non square no between them

Step-by-step explanation:

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Answer 2

The non-square number lies between the pair of 80 square and 81 square is 160.

Given,

The numbers = 80² and 81².

To Find,

The non-square number.

Solution,

In the given question, we will use the formula of Arithmetic progression.

In an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d.

Now, we will find the square of 80 and 81.

80² = 6400

81² = 6561

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

This is an arithmetic progression.

Now, we will find the number of non-square numbers.

First term = a = 6401

Common Difference = d = 6402 - 6401 = 1

Let 6560 be 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 lying between 80 square and 81 square is 160.

The non-square number lies between the pair of 80 square and 81 square is 160.

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