Question

Explain how 2 is an irrational no. step by step explaination ​

Answer 1

Answer:

Proof that root 2 is an irrational number.

Answer: Given √2.

To prove: √2 is an irrational number. Proof: Let us assume that √2 is a rational number. So it can be expressed in the form p/q where p, q are co-prime integers and q≠0. √2 = p/q. ...

Solving. √2 = p/q. On squaring both the side we get, =>2 = (p/q)2 => 2q2 = p2……………………………..(1)

The square root of 2 is "irrational" (cannot be written as a fraction) ... because if it could be written as a fraction then we would have the absurd case that the fraction would have even numbers at both top and bottom and so could always be simplified.

Answer 2

Rational Number is defined as the number which can be expressed as a fraction
q/p
​
for any integers p,q. An irrational number is a number which cannot be expressed as a fraction
q/p
​
for any integers p/q.
In rational numbers, both numerator and denominator are whole numbers, where the denominator is not equal to zero. While an irrational number cannot be written in a fraction.
Also, the decimal expansion of a rational number is terminating or non-terminating repeating while, that of an irrational number is non-terminating non-repeating.