Asked by meoww :3
Which of the following numbers is irrational?
a fraction with numerator negative 9 and denominator 5, a fraction with numerator square root of 5, a fraction with numerator 7 and denominator 3, square root of 9
Group of answer choices
a fraction with numerator negative 9 and denominator 5
a fraction with numerator square root of 5
a fraction with numerator 7 and denominator 3
square root of 9
a fraction with numerator negative 9 and denominator 5, a fraction with numerator square root of 5, a fraction with numerator 7 and denominator 3, square root of 9
Group of answer choices
a fraction with numerator negative 9 and denominator 5
a fraction with numerator square root of 5
a fraction with numerator 7 and denominator 3
square root of 9
Answers
Answered by
GPT-4o mini
To determine which of the given numbers is irrational, let's analyze each option:
1. **A fraction with numerator negative 9 and denominator 5**: This is \(-\frac{9}{5}\), which is a rational number since it can be expressed as a fraction of two integers.
2. **A fraction with numerator square root of 5**: This is \(\frac{\sqrt{5}}{1}\). The square root of 5 is an irrational number, so this fraction represents an irrational number.
3. **A fraction with numerator 7 and denominator 3**: This is \(\frac{7}{3}\), which is a rational number since it can also be expressed as a fraction of two integers.
4. **Square root of 9**: This is \(\sqrt{9} = 3\), which is a rational number since it can be expressed as the integer 3.
The only number from the list that is irrational is **a fraction with numerator square root of 5**.
1. **A fraction with numerator negative 9 and denominator 5**: This is \(-\frac{9}{5}\), which is a rational number since it can be expressed as a fraction of two integers.
2. **A fraction with numerator square root of 5**: This is \(\frac{\sqrt{5}}{1}\). The square root of 5 is an irrational number, so this fraction represents an irrational number.
3. **A fraction with numerator 7 and denominator 3**: This is \(\frac{7}{3}\), which is a rational number since it can also be expressed as a fraction of two integers.
4. **Square root of 9**: This is \(\sqrt{9} = 3\), which is a rational number since it can be expressed as the integer 3.
The only number from the list that is irrational is **a fraction with numerator square root of 5**.
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