Question

prove that √2 is an irrational number​

Answer 1

Answer:

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Step-by-step explanation:

PLEASE REFER TO THE ATTACHMENT

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Answer 2

Answer:

Hey there

Let us assume that root 2 is an rational number,

then, √2 = a/b

where A and B are positive integers and b is not equal to zero,

squaring both the sides

2 = a^2/b^2

2b^2 = a^2

this means that 2 is a factor of a,

now let a = 2c

squaring both the sides

a^2 = 4c^2

2b^2 = 4c^2

b^2 = 2c^2

this means that 2 is a factor of B

Therefore 2 is the common factor of a and b

but it contradicts the fact that A and B does not have any common factor

Thus our assumption is wrong

Hence root 2 is an irrational number