5+√3 it is irrational number prove that

1.	5+√3 it is irrational number prove that
Answer» Your Welcome ? Let ✓3 be rational Therefore ✓3 = a/b where a and b are co primes From the above eq ✓3b = a This shows that ✓3 is a. factor of a This contradicts the fact that a is a co prime -1st statement b= a /✓3 This also shows that ✓3 is a factor of b This contradicts the fact that b is a co prime -2nd statement From the statements 1 and 2 we can conclude that ✓ 3 is not a rational number and therefore our assumption is wrong.Hence ✓ 3 is irrational The addition of a rational and an irrational number is always irrational So therefore 5+✓3 is also irrationalHence proved Sssssu

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