prove that √2+√5 is irrational step by step explanation
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Let √2+√5 be rational no.
√2+√5 = p /q ( where p and q are co prime and q ≠0)
Squaring both side
(√2+√5)² = (p/q)²
2 +2√10 + 5 = p²/q²
7 + 2√10 = p²/q²
2√10 = p²/q² - 7
√10 = p²/2q² - 7/2
.
In LHS there is Irrational no. and in RHS there is rational no. It is not possible. This contradiction arise due to our wrong assumption. Thus our assumption is wrong and √2+√5 is Irrational no.
Hence proved.
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