Question

Prove that V2 + √7 is an irrational number.
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Answer 1

Answer:

$\sqrt{2} + \sqrt{7} = \sqrt{2 + 7} \\ = \sqrt{9} \\ = 3 \\ \\ so \: \sqrt{2} + \sqrt{7} \: is \: not \: an \: irrational \: number$

Answer 2

Answer:

Let us assume that 7

2

is rational number.

7

2

×

7

7

=

7

2

7

is rational number .

which is only possible is

7

2

7

is rational and √7 is rational.

But the fact is

7

is an irrational.

which contradicts to our assumption.

$

7

2

is an irrational number. hence proved.