RS Aggarwal Solutions Class 8 Chapter-3 Squares and Square Roots (Ex 3H) Exercise 3.8

Q: 3. What are the properties of Square numbers?

The properties of a square number are-Square numbers cannot end any other than the digits 0, 1, 4, 5, 6, and 9. The number of zeros at the end of any square number is always even. The squares of even numbers are always even, and the squares of odd numbers are always odd in value.Square numbers are always positive because two negative signs multiplied by each other turn into positive signs. The square root of any square number will always be a whole number.

Q: 4. What are the properties of square root numbers?

The properties of a square root number are-Only 1 perfect square root exists for a perfect square number.The square root of an even perfect square is always even.A perfect square that is odd will always have an odd square root.A perfect square cannot be negative and thus the square root of a negative number is not defined.Numbers with unit digits as 1, 4, 5, 6, or 9 will always have a square root.If the unit digit of a number is either one of 2, 3, 7, or 8 then a perfect square root is not possible.A square root is only possible if there are an even number of zeros.Two square roots can always be multiplied. Two same square roots are multiplied to give a non-square root number.

RS Aggarwal Solutions

RS Aggarwal Solutions Class 8 Chapter-3 Squares and Square Roots (Ex 3H) Exercise 3.8

Free PDF Download of RS Aggarwal Solutions Class 8 Chapter-3 Squares and Square Roots (Ex 3H) Exercise 3.8

All Exercise 3.8 Questions with Solutions for Class 8 Maths RS Aggarwal to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.

Vedantu is a platform that provides free NCERT Solution and other study materials for students. Science Students who are looking for NCERT Solutions for Class 8 Science will also find the Solutions curated by our Master Teachers Helpful.

Question: How to download Class 8 RS Aggarwal Chapter 3 Solutions

Answer: Students can download Class 8 RS Aggarwal Chapter 3 Squares and Square Root Solutions at Vedantu’s official website.

Overview of Class 8 Chapter 3

The Square of a number is the value that is obtained when it is multiplied by itself or given the exponential power. The square root of any number is the number that the student needs to multiply by itself to get the original number. The square root of a given number is an inverse operation of squaring the number. If 'x' is the square root of 'y', it implies that x×x=y

The square of any given number is always one 'Positive Value'. All numbers have two square roots-

one positive value
one negative value

For example, square roots of 9 are 3 and -3, but commonly, only the positive value is used as the square root.

Methods to find Square Roots of Given Numbers :

There are 4 major methods to find the Square Root of a given number. These are-

Repeated Subtraction Method of Square Root
Square Root by Prime Factorization Method
Square Root by Estimation Method
Square Root by Long Division Method

FAQs on RS Aggarwal Solutions Class 8 Chapter-3 Squares and Square Roots (Ex 3H) Exercise 3.8

1. What is the Repeated Subtraction Method of Square Root?

To perform the Repeated Subtraction Method of Square Root to find the Square root of any given number, the student has to subtract the consecutive odd numbers from the given number. This should be done till it reaches 0. The number of times it got subtracted is the square root of the given number. This method will only work with perfect square numbers. For example, to find out the square root of 9 using this method-

9-1=8

8-3=5

5-5=0

The number '9' was subtracted 3 times, hence the square of 9 is 3.

2. What is the Square Root by Estimation Method?

Estimation is a method where the student reaches a reasonable guess of the actual value to make calculations easier. To perform the Estimation or Approximation Method of Square Root to find the Square root of any given number, the student has to find the nearest perfect square number of the given number first and then estimate by eliminating other possibilities. This is a very long and time-consuming method and students should avoid using the Square Root by Estimation Method to find square roots of a given number.

3. What are the properties of Square numbers?

The properties of a square number are-

Square numbers cannot end any other than the digits 0, 1, 4, 5, 6, and 9.
The number of zeros at the end of any square number is always even.
The squares of even numbers are always even, and the squares of odd numbers are always odd in value.
Square numbers are always positive because two negative signs multiplied by each other turn into positive signs.
The square root of any square number will always be a whole number.

4. What are the properties of square root numbers?

The properties of a square root number are-

Only 1 perfect square root exists for a perfect square number.
The square root of an even perfect square is always even.
A perfect square that is odd will always have an odd square root.
A perfect square cannot be negative and thus the square root of a negative number is not defined.
Numbers with unit digits as 1, 4, 5, 6, or 9 will always have a square root.
If the unit digit of a number is either one of 2, 3, 7, or 8 then a perfect square root is not possible.
A square root is only possible if there are an even number of zeros.
Two square roots can always be multiplied.
Two same square roots are multiplied to give a non-square root number.

5. What are perfect square numbers?

Perfect Squares Numbers are numbers that are a result of squaring an integer or whole number. In other words, perfect square numbers are those which can be expressed as the multiplication of an integer by itself. These are the second exponent of an integer. Some examples of perfect square numbers are 25, 9, 81, etc. 81 is a perfect square number because it can be expressed as the product of 9 by itself. To know more about other properties of square numbers, visit Vedantu's website.