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Prove that √3 is irrational . |
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Answer» Let us assume to the contrary that √3 is a rational number.It can be expressed in the form of p/qwhere p and q are co-primes and q≠ 0.⇒ √3 = p/q⇒ 3 = p2/q2 (Squaring on both the sides)⇒ 3q2 = p2………………………………..(1)It MEANS that 3 DIVIDES p2 and also 3 divides p because each factor should appear two times for the square to exist.So we have p = 3rwhere r is some integer.⇒ p2 = 9r2………………………………..(2)from equation (1) and (2)⇒ 3q2 = 9r2⇒ q2 = 3r2Where q2 is multiply of 3 and also q is MULTIPLE of 3.Then p, q have a common factor of 3. This runs contrary to their being co-primes. Consequently, p / q is not a rational number. This demonstrates that √3 is an IRRATIONAL number.Step-by-step explanation:plz mark me as brainliest and thank my answer |
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