Question

prove that the sum of a rational number and an irrational no is an irrational no​

Answer 1

Answer:

Step-by-step explanation:

Assume that a is rational, b is irrational, and a+b is rational. Since a and a+b are rational, we can write them as fractions.

Let a = c/d

And a + b = m/n

​ Substituting a = c/d    in a + b = m/n  gives the following:

c/d + b = m/n

Now, let's subtract  c/d  from both sides of the equation.

b = m/n - c/d  

or,  b = m/n + (-c/d)

Since the rational numbers are closed under addition, b = m/n + (-c/d)  is a rational number. However, the assumptions said that b is irrational, and b cannot be both rational and irrational. This is our contradiction, so it must be the case that the sum of a rational and an irrational number is always irrational.

Hope it helps you :)

Answer 2

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Step-by-step explanation:

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