Squares and Square Roots Class 8 Notes available here is specially designed by math experts who have taken extra care to use simple language and style so that students can understand concepts easily and quickly. Chapter 6 notes are a great reference tool and will help students to quickly go through or revise all the important topics before the exams as well as score better marks. Besides, some of the key topics covered in the notes include;
- Square Number
- Properties of Square Numbers
- Finding the Square of a Number
- What is a Square Root?
- Finding The Square Root of A Number
- Important Questions
A square of a number is the product of some number with itself. For example, take any natural number, let’s say m and express it as n2. Here n is a natural number and thus m can be labelled as a square number. The other name for square numbers is perfect squares.
Properties of Square Numbers
Some of the properties of square numbers are;
- Square numbers always end with 0, 1, 4, 5, 6 or 9 at the unit’s place.
- If a number has 4 or 6 in its unit’s place, then the square of that number will end with 6.
- At the end of any square number, there will always be an even number of zeros.
- When two consecutive triangular numbers are combined it gives a square number.
- Square numbers are usually the sum of odd numbers in successive order starting from 1.
- The summation of two consecutive natural numbers gives a square number.
Finding the Square of a Number
There are several ways to find the square of a number. Some of them are given below;
- Divide a number into two parts, such that the square of those numbers is known. For example, x2 = (a +b)2, where (a + b) = x and values of the square of a and b are known.
- If any number ends with 5, refer (a5)2 = a x (a+1) x 100 + 25
- Pythagorean triplets
When the sum of two square numbers is a square number, all the three numbers in the equation form a Pythagorean triplet.
What is a Square Root?
The square root is a value that, when it is multiplied by itself, produces a specified quantity for a given number. A square root is the inverse operation of squaring.
Finding The Square Root of A Number
- Method of repeated subtraction Here, the square number is usually subtracted from successive odd natural numbers starting from 1. It is done until the result achieved is 0.
- Method of Prime Factorisation
- Find the square root of √324 by the prime factorization method.
- Get the prime factors of 324. Usually it is 324 = 2 x 2 x 3 x 3 x 3 x 3.
- Now pair the prime factors after which we get 324 =(2 × 2) × (3 × 3) × (3 × 3) = (2 × 3 × 3).
- Now, √324 = 2 × 3 × 3 = 18.
- Division Method
This method involves several steps;