Q14 :} Prove that root p+ root q is irrational if p and q are prime numbers.
Answers
Answered by
9
Answer:
Let √p +√q is rational number
than a/b = (√p +√q)
(a/b - √p) = √q
(a - b√p) / b = √q
squaring both sides
a^2+b^2 p - 2ab√p = q
a^2+b^2 p - q = 2ab√p
(a^2+b^2 p - q) /2ab = √p
left side is rational and right side is irrational
it is contradiction
so, √p +√q is irrational number
Answered by
0
Answer:
IRRATIONAL
Step-by-step explanation:
Let √p +√q is rational number
than a/b = (√p +√q)
(a/b - √p) = √q
(a - b√p) / b = √q
squaring both sides
a^2+b^2 p - 2ab√p = q
a^2+b^2 p - q = 2ab√p
(a^2+b^2 p - q) /2ab = √p
left side is rational and right side is irrational
it is contradiction
so, √p +√q is irrational number
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