Question

Prove that Sqrt(8) is irrational

Answer 1

suppose rt8=a/b with integers a,b and gcd(a,b)=1(meaning the ratio is simplisfied)

then8=asq/BST

and 8bsq=asquith

this implies 8 divides asq which also means such that:

a=8p

and

rt8= 8p/b

which implies

8=64psq/bsq

which is:

1/8=psq/bsq

or:

bsq/psq=8

which implies

bsq=8psq

which implies 8divides bsq which means 8divides b.

8divides a,and 8divide b,which is a contradiction because gcd (a,b)=1

therefore the square root of 8is irrational

Answer 2

Answer:

Step-by-step explanation: let root 8 be a rational number which can be expressed in form of p/q where p and q are coprime integers and q not equal to 0.

p/q= root 8

p/q=2root2

p/2q=root 2.........(1)

We know that,

Root2 is irrational no.

So in equation (1),

Rational no. Cannot be equal to irrational no.

Hence our supposition is wrong and root 8 is irrational no. Only