Question

Which type of number is (2 + √5)?

a. Rational number

b. Irrational number

c. Integer

d. Not a real number​

Answer 1

Answer:

b irrational

................

Answer 2

Answer:

irrational

Irrational. Sum of a rational and an irrational number is always irrational.

Proof by contradiction:

Let's say x is a rational no and y is an irrational no

Suppose: x+y is rational

Let x+y = z

So z is supposedly a rational no.

Now sum of 2 rational numbers is always rational.

Let's add -x to z, as x is rational so -x is also rational.

z-x = x+y-x = y

But we know that y is irrational.

Hence x+y must be irrational

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