 Most Affordable JEE | NEET | 8,9,10 Preparation by Kota's Top IITian Doctor Faculties

# NCERT Solutions for Class 8 Maths Chapter 5 Exercise 5.1 Square and Square Roots - PDF Download NCERT solutions for class 8 maths chapter 5 ex 5.1 Square and Square Roots describes the properties of square numbers such as all square numbers ending with a zero,1,4,5, 6, or 9 and that they have an even number of zeros at the end as well as some interesting patterns of square numbers. Class 8 maths chapter 5 exercise 5.1 NCERT solutions, students will also learn that if you cannot write a natural number as the sum of successive odd natural numbers that begin with 1, then the natural number is not a perfect square.

In addition, this exercise briefly discusses questions such as how to calculate the sum of consecutive natural numbers and the product of two consecutive even and odd natural numbers. Ex 5.1 class 8 maths chapter 5 Square and Square Roots NCERT solution consists of 9 questions which are based on the concepts mentioned above. eSaral's NCERT solutions are created by our subject experts using a step-wise approach. Class 8 maths NCERT solutions available here in PDF format which help students to prepare for their exam. Students can download the free PDF from eSaral and practice all the questions of ex 5.1.

## Topics Covered in Exercise 5.1 Class 8 Mathematics Questions

Ex 5.1 class 8 maths ch 5 Squares and Square Roots is based on the topics of properties of square numbers and some interesting patterns of square numbers.

 1 Properties of Square Numbers 2 Some More Interesting Patterns Adding triangular numbers Numbers between square numbers Adding odd numbers A sum of consecutive natural numbers Product of two consecutive even or odd natural numbers Some more patterns in square numbers
1. Properties of Square Numbers

• You can see that the square numbers end with 0, 1, 4, 5, 6 or 9 only. None of the square numbers ends with 2, 3, 7 or 8.

• Any number that has 1 or 9 in its one’s place will always have a square ending with 1.

• Any number that has 4 or 6 in its unit’s place, its square will always end with 6.

• Any number that has zero as its unit place, the square of that number will always have an even number of zeros at the end.

2.  Some More Interesting Patterns

• Adding triangular numbers - If the dotted pattern can be arranged in a triangular shape, then the numbers are referred to as triangular numbers. If we add two consecutive triangular numbers, we get a square number.

• Numbers between square numbers - If we have two consecutive numbers n and n + 1, then there are (2n) non perfect square numbers between their square numbers.

• Adding odd numbers - The sum of the first n natural odd numbers is n2.

Any square number must be the sum of consecutive odd numbers starting from 1. if any natural number which is not a sum of successive odd natural numbers starting with 1, then it will not be a perfect square.

• A sum of consecutive natural numbers - Every square number is the summation of two consecutive positive natural numbers. For example, if you are finding the square of n to identify two consecutive natural numbers, you can utilize the formula:

First number = n2-1/2

Second number = n2+1/2

• Product of two consecutive even or odd natural numbers - If we have two consecutive even or odd numbers (a+1) and a -1, the product will be (a2-1).

• Some more patterns in square numbers - This section will teach more patterns in square numbers.

## Tips for Solving Exercise 5.1 Class 8 Chapter 5 Square and Square Roots

Here, our subject experts have provided some useful tips to solve ex 5.1 questions. You can check these tips mentioned below.

1.  Ex 5.1 class 8 maths solutions will appear simple to the students as long as they pay attention to the calculation part of the exercise.

2. You will also need to have good mental math skills to quickly solve the exercise questions.

3. NCERT solutions class 8 maths chapter 5 ex 5.1 helps in developing good observational skills which will help the students to notice the patterns that square numbers have. Good observational skills will help the students when they encounter different numbers as they will be able to remember what they need to do if they are able to identify and comprehend the number patterns.

## Importance of Solving Ex 5.1 Class 8 Maths Chapter 5 Square and Square Roots

NCERT solutions class 8 maths chapter 5 ex 5.1 helps students to gain a good understanding of the square and square roots concepts. Let’s discuss some of the key benefits of solving ex 5.1 class 8 maths solutions.

1. Students of class 8 will get a clear idea of solving the questions associated with square and square roots by going through the solutions of class 8 maths chapter 5 ex 5.1.

2. All the question answers are presented in an easy-to-understand format so that students can grasp the concepts.

3. NCERT class 8 maths solutions are available here in PDF format for students to download and use offline for future reference.

4. eSaral’s subject matter experts provide an in-depth solution of NCERT class 8 maths ex 5.1 that the students can easily understand.

Question 1. Write the properties of square numbers?

Answer 1. The properties of square numbers are:

1. You can see that the square numbers end with 0, 1, 4, 5, 6 or 9 only. None of the square numbers ends with 2, 3, 7 or 8.

2. Any number that has 1 or 9 in its one’s place will always have a square ending with 1.

3. Any number that has 4 or 6 in its unit’s place, its square will always end with 6.

4. Any number that has zero as its unit place, the square of that number will always have an even number of zeros at the end.

Question 2. Where can I find the NCERT solutions for class 8 maths chapter 5 ex 5.1?

Answer 2. You can find the NCERT solutions for class 8 maths chapter 5 ex 5.1 on eSaral website. These solutions are available in PDF format which you can download and practice ex 5.1 questions.