Prove that root 3 is irrational, Class10 Mathematics [ Real Numbers]

Subscribe go-to playlist for more topics Irrational numbers are subset of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers denominator q is not equal to zero (q ≠ 0). Let us assume that 1/√2 is a rational number. Then, 1/√2 = a/b, where a and b have no common factors other than 1. Here's a breakdown of the process with an example: 1. The Concept: Irrational Numbers: Real numbers that cannot be expressed as a simple fraction (p/q) where 'p' and 'q' are integers and 'q' is not zero. Proof by Contradiction: You start by assuming the opposite of what you want to prove. If the assumption leads to a logical inconsistency (a contradiction), then the original assumption must be false, and therefore the opposite statement is true. General Steps for Proving Irrationality: 1. Assume Rationality: Start by assuming the number you want to prove irrational is rational (can be written as a fraction p/q). 2. Manipulate the Equation: Use algebraic manipulations to derive an equation that relates the assumed rational representation to properties of integers. 3. Look for a Contradiction: Analyze the equation to see if it leads to a contradiction, such as showing that two co-prime numbers share a common factor or that a number is both even and odd. 4. Conclude Irrationality: If a contradiction is found, then the initial assumption that number is rational must be false, and therefore number is irrational. #viralvideo #study #maths