Question

prove root2 irrational

​

Answer 1

Step-by-step explanation:

pls look into this .....

Answer 2

ANSWER:

• √2 is an Irrational number.

GIVEN:

• Number = √2

TO PROVE:

• √2 is an irrational number.

SOLUTION:

Let √2 be a rational number which can be expressed in the form of p/q where p and q have no other common factor than 1.

=> √2 = p/q

=> √2q = p

Squaring both the sides we get:

=> (√2q)² = (p)²

=> 2q² = p². ....(i)

• 2 divides p²
• Then 2 divides p. ....(ii)

Let p = 2m in eq(i) we get,

=> 2q² = (2m)²

=> 2q² = 4m²

=> q² = 2m²

• 2 divides q²
• Then 2 divides q. ...(iii)

From eq(i) and (iii) we get;

• 2 is the common factor of p and q .
• Thus our contradiction is Wrong.
• √2 is an Irrational number.