Question

The square root of 2 is a rational number.
True
False

Answer 1

False

Answer 2

TRUE!!!!

Answer 3

Assume that √2 is a rational number. Then there are integers a and b such that a is coprime to b and √2 = a / b. In other words, √2 can be written as an irreducible fraction.

-The value of b cannot be 1 as there is no integer a the square of which is 2.
-There must be a prime p which divides b and which does not divide a otherwise the fraction would not be irreducible.
-The square of a can be factored as the product of the primes into which a is factored but with each power doubled.
-Therefore by unique factorization the prime p which divides b, and also its square, cannot divide the square of a.
-Therefore the square of an irreducible fraction cannot be reduced to an integer.
-Therefore the square root of 2 cannot be a rational number.

Answer 4

my bad. lol

Answer 5

lol ya it's TRUE ;)

Answer 6

false.

Answer 7

true