Question

prove that root 3 is irrational
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Answer 1

Answer:

let be assume that √3 is a rational number

∴ it can be written in the form of p/q

√3 = p/q (where q ≠ 0 and p and q are

co- prime positive integers)

√3q = p

squaring both side

3q² = p² ⇒ (1)

p² is divisible by 3

∴ p is also divisible by 3

∴ 3c = p

squaring both side

9c² = p² ⇒ (2)

from (1) and (2)

9c² = 3q²

3c² = q²

q² is divisible by 3

∴ q is also divisible by 3

therefore, 3 is a common factor of p and q

                but it is contradict that p and q are co prime

                positive integers

∴ our assumption is wrong and √3 is an irrational

 number

hence proved        

Step-by-step explanation:

Answer 2

Step-by-step explanation:

hope this answer helps you