Question

Show 2 root 9 is irrational

Answer 1

Step-by-step explanation:

2√9 is rational bcoz √9=±3

so 2√9=2×(±3)=6 or -6

so 2√9 is rational

Answer 2

Answer:

Let root 2 be a rational no. then according to the definition of rational numbers,

root 2 =p/q

2=p2/q2

2q2=p2

2 divides p

Now we have got our first equation.

The above statement shows that p must be a factor of 2, so,

Let p =2m

Now we will put the value of p in the first equation.

2q2 = (2m)2

2q2=4m2

q2= 2m2

According to the theorem of rational numbers, rational numbers should only have common factor 1.

But the above equation has a common factor 2 which shows that it is a rational number.

Hence proved that root 2 is an irrational number.

Hope it helps u