Question

Given that √2 is irrational prove that 2+√2 is rrational number.​

Answer 1

Answer:

2+ √2 is an irrational number as any rational no. + irrational no. is irrational.

Step-by-step explanation:

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Answer 2

Answer:

Given that

2

is irrational.

We know that the theorem The product of any irrational number with a rational number is irrational.

So, since we know 3 is a rational number, 3

2

is irrational.

(3=

1

3

;1



=0)

Now we know that 3

2

is irrational.

Theorem: The sum of a rational number with an irrational number is irrational.

So, since we know 5 is a rational number, 5+3

2

is irrational.

(5=

1

5

;1



=0)

Thus we proved that 5+3

2

is an irrational number.