Show that 4-root3 is irrational
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1
Answer:
Yes because 4 root 3 doesn't has square value
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0
Answer:
Let us assume to the contrary that root3 is rational
Where a and b are integers, a and b are coprimes, b is not equal to 0.
Squaring on both sides, we get
a^2 is divisible by 3
a is also divisible by 3 (1)
Let a=3c [c is an integer]
Squaring on both sides, we get
b^2 is divisible by 3
b is also divisible by 3(2)
From (1) and (2),a and b have a common factor 3 other than 1
Therefore, a and b are not coprimes
This contradiction arisen because of our wrong assumption that root3 is rational
Therefore, conclude root3 is irrational
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