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

1 answer

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 the ratio of two integers).

  2. A fraction with numerator square root of 5: This can be expressed as \(\frac{\sqrt{5}}{1}\). Since \(\sqrt{5}\) is not a perfect square, it is irrational; thus, this entire fraction is irrational.

  3. A fraction with numerator 7 and denominator 3: This is \(\frac{7}{3}\), which is a rational number.

  4. Square root of 9: This evaluates to \(3\), which is a rational number.

Based on this analysis, the number that is irrational is:

A fraction with numerator square root of 5.

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