Ex.6.1 Q9 Squares and Square Roots Solutions - NCERT Maths Class 8

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Question

How many numbers lie between squares of the following numbers?

(i) \(12\; \text{ and} \; 13\) 

(ii) \(25\; \text{and} \; 26\)   

(iii) \(99\; \text{and} \; 100\)

Text Solution

What is known?

Numbers

What is uknown?

How many number lie between squares of given number.

Reasoning:

There lies “\(2n\)” number between the square of the number \(n\) and \((n+1)\)

Steps:

(i) \(12\; \text{ and} \; 13\)

Here,\( n=12\) gives \(2 \times 12 = 24\), i.e., \(24\) numbers between \({\left( {12} \right)^2}\) and \({\left( {13} \right)^2}\)

(ii) \(25\; \text{and} \; 26\)

Here, \(n=25\) gives \(2 \times 25 = 50\), i.e., \(50\) numbers. between \({\left( {25} \right)^2}\) and \({\left( {26} \right)^2}\)

(iii) \(99\; \text{and} \; 100\)

Here, \(n=99\) gives \(2 \times 99 = 198\), i.e., \(198\) numbers between \({\left( {99} \right)^2}\) and \({\left( {100} \right)^2}\)