prove that √5+√11 is rational
Answers
Let us consider √5 + √11 is not irrational
then it becomes √5 + √11 is a rational
we know that
p/q where p , q belongs to integers and q ≠ 0
Squaring on both sides
(√5 + √11 ) 2 = ( p/q ) 2
Use ( a + b ) 2 formula
(√5)2 + (√11)2 + 2 × √5 × √11 = p2 / q2
5 + 11 + 2 × √55 = p2 / q2
16 + 2 × √55 = p2 / q2
2 × √55 = p2 / q2 - 16 / 1
√55 = p2 - 16 q2 / q2
LHS = √11 where it is irrational because " 11 " is
not a perfect square .
RHS = p2 - 16 q2 / q2
It becomes rational because it is in the form of p/q
Our contradiction is wrong
Our Assumption is wrong
√5 + √11 is an irrational
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Answer:
well it's not ..u can also do it by as root 5 + root 11=5.5526....hence it can be written in p/q form where p nd q are integers and q is not equal to zero ...so hence it's rational