Let's evaluate each of the given numbers to determine if they are irrational.
1. Absolute value of -7, denoted as [tex]\(|-7|\)[/tex]:
The absolute value of a negative number is a positive number. So, [tex]\(|-7| = 7\)[/tex].
- Since 7 can be expressed as the fraction [tex]\(\frac{7}{1}\)[/tex], it is a rational number because it is the ratio of two integers.
2. Square root of 121, denoted as [tex]\(\sqrt{121}\)[/tex]:
To find [tex]\(\sqrt{121}\)[/tex], we need to determine what number, when multiplied by itself, equals 121.
- [tex]\(\sqrt{121} = 11 \cdot 11 = 121\)[/tex], thus [tex]\(\sqrt{121} = 11\)[/tex].
- Since 11 is an integer, it can be expressed as the fraction [tex]\(\frac{11}{1}\)[/tex], making it a rational number.
3. Decimal number 0.45:
A decimal number can be assessed for its rationality by checking if it can be expressed as a fraction of two integers.
- 0.45 can be expressed as the fraction [tex]\(\frac{45}{100}\)[/tex], and can be simplified to [tex]\(\frac{9}{20}\)[/tex].
- Since it can be written as a fraction of two integers, 0.45 is a rational number.
An irrational number is one that cannot be expressed as a fraction of two integers, having a non-repeating, non-terminating decimal expansion. After evaluating each of the given numbers:
- [tex]\(|-7| = 7\)[/tex], which is a rational number.
- [tex]\(\sqrt{121} = 11\)[/tex], which is a rational number.
- [tex]\(0.45\)[/tex], which is a rational number.
Therefore, none of the numbers provided ([tex]\(|-7|\)[/tex], [tex]\(\sqrt{121}\)[/tex], 0.45) are irrational.
