20DATE:PAGE NOprove that the following core irrational numbe32

1.	20DATE:PAGE NOprove that the following core irrational numbe32
Answer» To prove 1/√2 is irrational Let us assume that√2 is irrational 1/√2 = p/q(where p and q are co prime) q/p =√2q =√2p squaring both sides q² = 2p² .....................(1) By theoremq is divisible by 2 ∴ q = 2c ( where c is an integer) putting the value of q in equitation 1 2p² = q² = 2c² =4c²p² =4c² /2 = 2c²p²/2 = c² by theorem p is also divisible by 2 But p and q are coprime This is a contradiction which has arisen due to our wrong assumption ∴1/√2 is irrational

Answer»

To prove 1/√2 is irrational

Let us assume that√2 is irrational

1/√2 = p/q(where p and q are co prime)

q/p =√2q =√2p

squaring both sides

q² = 2p² .....................(1)

By theoremq is divisible by 2

∴ q = 2c ( where c is an integer)

putting the value of q in equitation 1

2p² = q² = 2c² =4c²p² =4c² /2 = 2c²p²/2 = c²

by theorem p is also divisible by 2

But p and q are coprime

This is a contradiction which has arisen due to our wrong assumption

∴1/√2 is irrational

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