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Prove that √3 is an irrational …

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Prove that √3 is an irrational number.

Posted by Nandini Shekhar 5 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Angel Anjali 5 years, 6 months ago

Let us assume that √3 is a rational number. Then, as we know a rational number should be in the form of p/q where p and q are co- prime number. So, √3 = p/q { where p and q are co- prime} √3q = p Now, by squaring both the side we get, (√3q)² = p² 3q² = p² ........ ( i ) So, if 3 is the factor of p² then, 3 is also a factor of p ..... ( ii ) => Let p = 3m { where m is any integer } squaring both sides p² = (3m)² p² = 9m² putting the value of p² in equation ( i ) 3q² = p² 3q² = 9m² q² = 3m² So, if 3 is factor of q² q is divisible by 3 From this we can say p and q have a common factor 3 It contradicts our assumption p and q are co primes Therefore root 3 is an irrational number

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