Prove that √3 is irrational.
Answers
Heya,
If √5 is rational, then it can be expressed by some number a/b (in lowest terms). This would mean:
(a/b)² = 5. Squaring,
a² / b² = 5. Multiplying by b²,
a² = 5b².
If a and b are in lowest terms (as supposed), their squares would each have an even number of prime factors. 5b² has one more prime factor than b², meaning it would have an odd number of prime factors.
Every composite has a unique prime factorization and can't have both an even and odd number of prime factors. This contradiction forces the supposition wrong, so √5 cannot be rational. It is, therefore, irrational.
Answer:
√e3 is an irrational number as after taking out its root the answer is 1.7320508075688 and the decimal expansion of irrational numbers are non terminating , non repeating.
Step-by-step explanation:
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