Question

how many natural number between 97^2 and 122 ^2 are not perfect squares ?​

Answer 1

Answer:

Step-by-step explanation:

Given ,

97^2 = 97 × 97 = 9409

122^2 = 122 × 122 = 14884

Difference between 122^2 - 97^2 = 14884 - 9409 = 5475

Hence 5,475 natural numbers between 97^2 and 122^2 are not perfect squares.

Answer 2

The number of natural numbers between 97² and 122² which are not perfect squares is 5450.

To find the number of natural numbers which are not a perfect square we will first find the range of the numbers given

97² = 9409

122² = 14884

So the total numbers here are = 14884 - 9409 = 5475

Now we know that the lower limit here is the square of 97 and the upper limit here is the square of 122. Therefore the numbers between these two numbers which will be a perfect square will be

122 - 97 = 25

Therefore between 9049 and 14884, 25 numbers are perfect squares of a natural number.

Numbers which are not a perfect square = 5475 - 25 = 5450

Therefore 5450 numbers between  97² and 122² will not be a perfect square.