Question

prove that √3+√7 is an irrational number.
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Answer 1

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Answer 2

Answer:

We have to prove that 3+7 is irrational.

Let us assume the opposite, that 3+7 is rational.

Hence 3+7 can be written in the form ba where a and b are co-prime and b=0

Hence 3+7=ba

⇒7=ba−3

⇒7=ba−3b

where 7 is irrational and ba−3b is rational.

Since,rational= irrational.

This is a contradiction.

∴ Our assumption is incorrect.

Hence 3+7 is irrational.

Hence proved.