To determine whether the sum of [tex]\(4.2 + \sqrt{36}\)[/tex] is rational or irrational, let's analyze the numbers involved:
1. Identify the numbers:
- [tex]\(4.2\)[/tex] is a rational number. Rational numbers are numbers that can be expressed as a fraction or ratio of two integers, and 4.2 equals [tex]\( \frac{42}{10} \)[/tex].
- [tex]\(\sqrt{36}\)[/tex] needs to be simplified. The square root of 36 is 6, which is also a rational number because it can be expressed as [tex]\( \frac{6}{1} \)[/tex].
2. Sum of the numbers:
- Adding two rational numbers will always result in another rational number. Hence, adding [tex]\(4.2\)[/tex] and [tex]\(6\)[/tex] (which are both rational) will give a rational sum.
Therefore, the sum [tex]\(4.2 + \sqrt{36}\)[/tex] is rational.
The correct answer is [tex]\(1\)[/tex], indicating that the sum is rational.
