Question

Prove root2 is irrational

Answer 1

Answer:let us assume that root 2 is rational

Step-by-step explanation:

Answer 2

Let ✓2 be a rational number

So ✓2 =p/q(where p and q are co-prime numbers.

Squaring both the side

we get

2 = p²/q²

P²/2=q² or p²=2q²-----(1)

p²is divisible by 2 and p is also divisible by 2

We can write that

p=2m

Squaring both the side

p²=4m²

Substituting value of p²from equation (1)

we get

2q²=4 m²

or

q²=2m²

or q²/2= m²

q²is divisible by 2 and q is also divisible by 2

That means both q and p are divisible by 2

That is both have common factor as 2

but earlier we said that both are co-prime number

So this contradicts our assumption

So ✓2 is irrational number.

Hence proved

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