Question

How many numbers lie between the squares of the following numbers. () 15 and 16 (ii) 37 and 38 (iii) 51 and 52 (iv) 118 and 119

with step by step explanations ​

Answer 1

Solution

Verified by Toppe

(i) 12² = 144

13² = 169

169 - 144 = 25

So, there are 25 -1 = 24 numbers lying between 12² and 13²

(ii) 25² = 625

26²676

676-625 = 51

So, there are 51 - 1 = 50 numbers lying between 252 and 26²

(iii) 99² = 9801

100² = 10000

100009801 199

So, there are 199 - 1 = 198 numbers lying

between 992 and 100²

Answer 2

Step-by-step explanation:

Given :-

The squares of the following numbers

(i) 15 and 16

(ii) 37 and 38

(iii) 51 and 52

(iv) 118 and 119

To find :-

How many numbers lie between the squares of the following numbers?

Solution :-

(i)

Given numbers are 15 and 16

The squares of the numbers = 15² and 16²

=> 15² and (15+1)²

We know that

The number of natural numbers lie between n² and (n+1)² is 2n

We have n = 15 and n+1 = 15+1 = 16

The number of numbers lie between 15² and 16²

=> 2(15)

=> 30

(ii)

Given numbers are 37 and 38

The squares of the numbers = 37² and 38²

=> 37² and (37+1)²

We know that

The number of natural numbers lie between n² and (n+1)² is 2n

We have n = 37 and n+1 = 37+1 = 38

The number of numbers lie between 37² and 38²

=> 2(37)

=> 74

(iii)

Given numbers are 51 and 52

The squares of the numbers = 51² and 52²

=> 51² and (51+1)²

We know that

The number of natural numbers lie between n² and (n+1)² is 2n

We have n = 51 and n+1 = 51+1 = 52

The number of numbers lie between 51² and 52²

=> 2(51)

=> 102

(iv)

Given numbers are 118 and 119

The squares of the numbers = 118² and 119²

=> 118² and (118+1)²

We know that

The number of natural numbers lie between n² and (n+1)² is 2n

We have n = 118 and n+1 = 118+1 = 119

The number of numbers lie between 118² and 119²

=> 2(118)

=> 236

Answer :-

(I) 30

(ii) 74

(iii) 102

(iv) 236

Used formulae:-

The number of natural numbers lie between n² and (n+1)² is '2n'