Prove that √3+√5 is irrational
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→ √3 + √5
→ 1.732... + 2.236...
→ 3.961... [Non - Terminating nD Non - Repeating ]
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- √3 + √5
- It is a irrational number.
- √3 + √5
- First,
Let us assume that √3 + √5 is an rational number.
- √3 + √5 =
- where,
- a and b are co - primes and b
0.
- Now,
- Squarring on both sides,
- Taking LCM on RHS,
- Here, a and b are Integers.
Therefore,
is a rational number.
- But, this contradicts the fact that √3 + √5 is a irrational number.
Therefore,
- Our assumption is wrong.
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