Class 8th In this chapter-6, you are going to learn Squares and Square Roots. It is very beneficial for students since it aids them in scoring high marks in exams. These NCERT books provide solution modules with various shortcut hints and practical examples to explain all the exercises. As a student, you will learn various techniques to determine whether a given natural number is a perfect square are not.
Here you are going to learn in detail and step by step and help you to understand more effectively.
Table of contents in Book
- Square number
- How to find square number easily
- Pythagorean triples
- Square Root
- How to Find Square root
- Estimating Digits in the square Roots
Square Number:
The square of the number is the number that is multiplied by itself. A perfect square is the square of an integer. The square root of the number n written below is the number that produces n when multiplied by itself.
Example:
1=12
4=22
The numbers are 1, 4, 9, 16 .. are square numbers. These numbers are also called perfect squares.
How to find the square of Number easily:
(a+b)2 =a2 +2ab+b2 Example 232= (20+3)2 =400+9+120=529
Special Case
(a5)2
= a(a + 1) hundred + 25
All this solutions are in the book please refer the book
Pythagorean triplets
For the any natural number m > 1, we have (2m)2 + (m2 – 1)2 = (m2 + 1)2
So, 2m, m2 – 1 and m2 + 1 form a Pythagorean triplet Solved Example Finding a Pythagorean triplet in which one member is 12.
Solution
If we take m2 – 1 = 12
Then, m2 = 12 + 1 = 13
Then a value of m will not be an integer.
So, we try to take m2 + 1 = 12. Again the m2 = 11 will not give an integer value for m.
So, let us take 2m = 12
then m = 6
Thus, m2 – 1 = 36 – 1 = 35 and m2 + 1 = 36 + 1 = 37
Therefore, the required triplet is 12, 35, 37
Square Root
The Square root of a number is the number.whose square is given number
So we know that
m=n2
The square root of m
√m =n
A square root is denoted by the expression √
To Find Square root there are three methods:
- Finding square root through repeated subtraction
- Finding square root through prime factorization
- Finding square root by division method
These methods you can learn in NCERT months class 8th.
Estimating Digits in the Square Root
If the perfect square is of n-digits, then its square root will have n/2 digits if n is even or (n+ 1)/2
if n is odd Example Find some digits in the square root of the following numbers.
(i) 25921
(ii) 37249 Solution Here n is odd, so (n+1)/2 = 3
So three for digits will be present in the square root
Conclusion
Square and Square roots are a big part of math, especially Algebra. You will use square and square roots not only for the rest of the year, but for the rest of your mathematical career. You will continue to build on your knowledge of the subject of square and square Root by showing you different ways to use them to solve different types of problems.