Question

How many numbers lie between the square of 16 and 17?

Answer 1

Square root of 16 and 17
=16=2n
=16×2
=32
-Therefore,32 numbers lie between 256 and 289.
OR
square of 16= 256
square of 17=289

Hence,289-256=33-1=32

Answer 2

The number of numbers lie between 16² and 17² is 32

Given :

The numbers 16² and 17²

To find :

The number of numbers lie between 16² and 17²

Solution :

Step 1 of 2 :

Write down the given numbers

Here the given numbers are 16² and 17²

Step 2 of 2 :

Find number of numbers lie between 16² and 17²

16² = 256

17² = 289

The natural numbers lie between 16² and 17² are 257 , 258 , 259 , . . . , 288

This is an arithmetic progression

First term = a = 257

Common Difference = d = 258 - 257 = 1

Let 288 is the nth term of the AP

⇒ a + ( n - 1 )d = 288

⇒ 257 + ( n - 1 ) = 288

⇒ n + 256 = 288

⇒ n = 288 - 256

⇒ n = 32

The number of numbers lie between 16² and 17² is 32

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