Answer :
To determine whether [tex]\(\sqrt{169}\)[/tex] is rational or irrational, follow these steps:
1. Identify the given number under the square root: We have [tex]\(\sqrt{169}\)[/tex].
2. Compute the square root of 169:
[tex]\[ \sqrt{169} = 13 \][/tex]
3. Understand the properties of rational and irrational numbers:
- A rational number is a number that can be expressed as the quotient of two integers (i.e., it can be written as [tex]\(\frac{a}{b}\)[/tex], where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are integers and [tex]\(b \neq 0\)[/tex]).
- An irrational number cannot be expressed as the quotient of two integers. It has a non-repeating, non-terminating decimal expansion.
4. Determine if the result is an integer:
- The square root of 169 is 13.
- 13 is an integer.
5. Conclude the nature of the number:
- Since 13 is an integer, and integers are rational numbers (because any integer [tex]\(n\)[/tex] can be written as [tex]\(\frac{n}{1}\)[/tex], which fits the definition of a rational number).
Therefore, [tex]\(\sqrt{169} = 13\)[/tex] is a rational number.
The answer is:
[tex]\[ \text{Rational} \][/tex]
1. Identify the given number under the square root: We have [tex]\(\sqrt{169}\)[/tex].
2. Compute the square root of 169:
[tex]\[ \sqrt{169} = 13 \][/tex]
3. Understand the properties of rational and irrational numbers:
- A rational number is a number that can be expressed as the quotient of two integers (i.e., it can be written as [tex]\(\frac{a}{b}\)[/tex], where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are integers and [tex]\(b \neq 0\)[/tex]).
- An irrational number cannot be expressed as the quotient of two integers. It has a non-repeating, non-terminating decimal expansion.
4. Determine if the result is an integer:
- The square root of 169 is 13.
- 13 is an integer.
5. Conclude the nature of the number:
- Since 13 is an integer, and integers are rational numbers (because any integer [tex]\(n\)[/tex] can be written as [tex]\(\frac{n}{1}\)[/tex], which fits the definition of a rational number).
Therefore, [tex]\(\sqrt{169} = 13\)[/tex] is a rational number.
The answer is:
[tex]\[ \text{Rational} \][/tex]
