Question

Assertion -: 2+√6 is an irrational number . Reason -: sum of an rational number and an irrational number is always irrational . a- both assertion and reason are correct . b- assertion is true but reason is false . c- assertion is false but reason is true . d- both assertion and reason are false​

Answer 1

Answer:

Integers are the complete numbers, i.e. they are free of any decimal parts.

e.g. ...,−2,−1,0,1,2,...

Rational numbers are the numbers which can be expressed as a ratio of two integers. i.e. they can be written in the form of pq,(p,q)∈Z,q≠0.

Irrational numbers are the numbers which cannot be expressed as a ratio of two integers.

e.g. 2–√=1.4142135...,π=3.141592

Answer 2

Given,

Assertion: $\[2 + \sqrt 6 \]$ is an irrational number.

Reason: sum of a rational number and an irrational number is always irrational.

To find,

The correct option.

(a) Both assertion and reason are correct.

(b) Assertion is true but Reason is false.

(c) Assertion is false but Reason is true.

(d) Both assertion and reason are false​.

Solution,

Know that a rational number is a number in the form of $\[\frac{p}{q}\]$ where $\[q \ne 0\]$.

Similarly, an irrational number is one that cannot be represented as a simple fraction.

Therefore, $\[2 + \sqrt 6 \]$ is an irrational number.

Similarly, the sum of a rational number and an irrational number is always irrational, example

$\[\begin{array}{l} \Rightarrow 2 + \sqrt 6 \\ \Rightarrow 2 + 2.449\\ \Rightarrow 4.449\end{array}\]$

Hence, the correct option is (a) i.e. Both assertion and reason are correct.