Show that √3 is an irrational number.
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1
Answer:
ya this is irrational number
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2
Step-by-step explanation:
Let,
√3 be a / b
a and b are co - primes.
a and b have 1 as a common factor.
√3 = a / b
a = √3b
Squaring on both sides,
a² = 3b² ------> 1.
a² is divisible by 3.
Therefore, a is also divisible by 3.
a and 3c
Squaring on both sides,
a² = 9c² ------> 2.
From 1 and 2,
3b² = 9c²
Divide 3 on both sides,
b² = 3c²
b² is divisible by 3.
Therefore, b is also divisible by 3.
b = 3x
3 is a factor of b.
a and b are not co - primes, since they have 3 as a common factor. Our assumption is wrong.
Therefore,
√3 is an irrational number.
Hence proved.
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