Question

proof that root 2 is not a rational number​

Answer 1

Answer:

A proof that the square root of 2 is irrational. Let's suppose √2 is a rational number. Then we can write it √2 = a/b where a, b are whole numbers, b not zero. We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction.

Answer 2

Step-by-step explanation:

On the contrary let us assume that root 2 is not a rational number

… √2 is rational

… √2=p/q {where and q are coprime and q≠0

Now, √2=p/q

squaring both sides

2=p²/q²

q²=p²/2

So., p² is the factor of 2

p is a factor of 2 -------------->(a)

Let p=2m.

So, q²=(2m)²/2

q²=4m²/2

q²=2m

q²/2=m

So,q² is a factor of 2

q is also a factor of 2---------------->(b)

From (a) and (b)

both p and q are factors of 2 which is a contradiction to a assumption at p and q are coprime .

So, our supposition is wrong

So, √2 is an irrational number.

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