show that that root 3 + root 5 the whole square is an irrational number
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Show that that root 3 + root 5 the whole square is an irrational number.
Given:
- Let us assume to the contrary that √√ ia a rational number,
- Then there exists a and b co-prime integers.
Calculation:
√√
√
√
√=
√=
√
is a rational number.
- Then √ is also a rational number.
- But as we know √ is an irrational number.
- This is a contradiction.
- This contradiction has arisen as our assumption is wrong.
- Hence √√ is an irrational number.
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