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State if the statement is true or false: $− 3 + 6$ is a rational number.

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True

False

answer is A.

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Detailed Solution

We are given a real number as

− 3 + 6

.
We have to determine if it is a rational number or not.
It can be observed that the given number has two sub-parts, one is an integer, i.e., -3, and the second is a radical i.e.,

6

.
Now, we know that -3 is a rational number.
Next, if we observe

6

, it can be written as a product of its prime factors as follows,

6 = 2 × 3 = 2 × 3

Now, we know that

2

and

3

both are irrational numbers because they cannot be expressed in the form of

p q

, as their decimal expansion is both non-terminating and non-repeating.
So,

6

is an irrational number.
Thus, if we add -3 and

6

, we get an irrational number.
Therefore,

− 3 + 6

is an irrational number.
Hence, the given statement is false.
So, the correct option is 1.

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