Question

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Answer 1

Step-by-step explanation:

Let √2 is a rational no.

So,

√2=a/b

square both sides,

2=a²/b²

a²=2b²

Hence a² is divisible by 2.

So a is also divisible by 2.

Now let,

a=2c

sqaure both sides,

a²=4c²

2b²=4c² (as a²=2b²)

b²=2c²

b² is divisible by 2

so b is also divisible by 2.

a and b both are divisible by 2 but rational no. are in form of a/b in which a and b are co-prime.

So we arive at a contradiction.

hence, √2 is irrational no.

Let 3-√2 is rational.

3-√2= x

x-3 = -√2

3-x = √2

x is rational

so 3-x is rational

but √2 is irrational so

we arrive at a contradiction.

Hence 3-√2 is irrational.

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Answer 2

i hope this helps u dear friend ^_^