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Explain why the sum of a rational number and an irrational number is an irrational number?
Let R1 = rational number Let X = irrational number Assume R1 + X = (some rational number) We add -R1 to both sides, and we get: -R1 + x = (some irrational number) + (-R1), thus X = (SIR) + (-R1), which implies that X, an irrational number, is the sum of two rational numbers, which is a contradiction. Thus, the sum of a rational number and an irrational number is always irrational. (Proof by contradiction)
Is 0.05 a rational or irrational number?
It is a rational number.
Can you add irrational number and a rational to get a rational number?
If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.
What happens when a rational number is divided by an irrational number?
When a rational numbers is divided by an irrational number, the answer is irrational for every non-zero rational number.
Is a rational number times a irrational number?
Can be irrational or rational.1 [rational] * sqrt(2) [irrational] = sqrt(2) [irrational]0 [rational] * sqrt(2) [irrational] = 0 [rational]
