prove √2 is irrational..........
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Let √2 be rational number . so it can be written as p/q form where q≠0.
according to question:
==> √2 = p/q
=> √2q = p
squaring both sides :-
=>2q² = p²
now we can see that p² is even because it's multiple of 2.
so p can be written as : p = 2x
=> p² = 4x²
=> 2q² = 4x²
=> q² = 2x²
here we can see that q² is also even because its multiple of 2 ..so our contradiction is wrong because...
two even numbers cannot be relatively prime,..
Hence proved... √2 is an irrational.
______________________________
⭐Hope it will help you..
____________
Let √2 be rational number . so it can be written as p/q form where q≠0.
according to question:
==> √2 = p/q
=> √2q = p
squaring both sides :-
=>2q² = p²
now we can see that p² is even because it's multiple of 2.
so p can be written as : p = 2x
=> p² = 4x²
=> 2q² = 4x²
=> q² = 2x²
here we can see that q² is also even because its multiple of 2 ..so our contradiction is wrong because...
two even numbers cannot be relatively prime,..
Hence proved... √2 is an irrational.
______________________________
⭐Hope it will help you..
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