To determine whether the real number [tex]\(\sqrt{49}\)[/tex] is irrational, let us evaluate and analyze it carefully.
1. Identify the number inside the square root:
- We are dealing with the number 49.
2. Evaluate the square root:
- The square root of 49 is calculated as follows:
[tex]\[
\sqrt{49} = 7
\][/tex]
3. Classify the result:
- The result of the square root operation is 7, which is an integer.
4. Determine the nature of the number:
- Recall that a rational number is any number that can be expressed as a quotient of two integers, [tex]\( \frac{a}{b} \)[/tex] where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are integers and [tex]\( b \neq 0 \)[/tex].
- Since 7 can be expressed as [tex]\( \frac{7}{1} \)[/tex], it is considered a rational number.
Therefore, [tex]\(\sqrt{49}\)[/tex] is a rational number.
Given this analysis, the correct response to the statement "The real number [tex]\(\sqrt{49}\)[/tex] is irrational" is:
False
