Math, asked by aakankshachoudhary20, 1 year ago

Q14 :} Prove that root p+ root q is irrational if p and q are prime numbers.​

Answers

Answered by bns970
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 SILENCE0
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

Similar questions