Question

prove that √3 is irrational​

Answer 1

Step-by-step explanation:

Let us assume to the contrary that √3 is a rational number. where p and q are co-primes and q≠ 0. Consequently, p / q is not a rational number. This demonstrates that √3 is an irrational number.

Answer 2

Answer:

Let's us asume that the contrary that √3 is rational.

√3=a/b. [ a and b are co-prime]

√3b=a. [ squaring both sides]

3b square=a square. [a square is divisible by 3].................(I)

a=3c. [ c is any integer]

3b square= (3c) square

3b square=9c square

b square = 3c square [ b Square is divisible by 3]...............(ii)

by (i) and (ii)

a and b having common factor 3.

so this contradiction is arisen because our incorrect assumption.

then √3 is Irrational.

Step-by-step explanation:

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