Question

root2 is a irrational with proof explain?

Answer 1

i hope u get a answer
plz marks as a brainlist

Answer 2

hola amigo!

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

we will prove this by the method of contradiction or going against it.

so we us assume that √2 is a rational number.

we know that a rational number can be written in the form of p/q 
where both p and q are co- prime 

{ co-prime= the numbers which do that have factors other than 1 and the the number itself}

so,

√2 = $\frac{p}{q}$            ( where p and q are co- prime)
√2q= p
squaring both sides we get:
2q² = p²
now we see that 2 can divide p² so it can divide p too.
let us write p = 2c

now putting the value of p we get:

2q² = (2c)²
2q² = 4c²
q² = 2c²

now we see that 2 divides q² and q too.
so, let us write q= 2v

but, we thought that both p and q were co- prime.
now we have concluded that they both have factors other than one, i.e. 2
so this is our contradiction to the fact that √2 is rational.
therefore, it is irrational.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

hope it helps :)