Question

prove that 1 1by root 2is an irrational number
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Answer 1

Answers

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 = √2

q = √2p

squaring both sides

q² = 2p² .....................(1)

By theorem

q is divisible by 2

∴ q = 2c ( where c is an integer)

putting the value of q in equitation 1

2p² = q² = 2c² =4c²

p² =4c² /2 = 2c²

p²/2 = 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 2

Step-by-step explanation:

1/√2 = p/q 

q/p = √2

q     = √2p

squaring both sides

q²   = 2p²                                                  .....................(1)

By theorem 

q is divisible by 2

∴ q = 2c

2p² = q² = 2c² =4c²

p² =4c² /2 = 2c²

p²/2 = c² 

by theorem p is also divisible by 2

∴1/√2 is irrational

hope it helps:--

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