prove that √3 is irrational
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Step-by-step explanation:
Let (where p and q is a co-prime)
Squaring both the side in above equation
3 × q² = p²
If 3 is a factor of p²
Then, 3 will also be a factor of p
Let p=3m ----- (where m is a integer)
Squaring both sides we get
p² = (3m)²
p² = 9m²
Substitute the value of p²
3q² = p²
3q² = 9m²
Cube rooting both sides
q² = 3m²
If 3 is a factor of q²
Then, 3 will also be factor of q
Hence, 3 is a factor of p & q both
So, our assumption that p & q are co-prime is wrong.
So, √3 is an "irrational number". Hence proved.
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