Question

which numbers are irrational? select all that apply. options: -3i, 4i, √5, 5, 3+2i

Explanation:

Step1: Define irrational numbers

Irrational numbers are real numbers that cannot be written as a simple fraction $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$.

Step2: Analyze each number

• $-3i$: Imaginary number, not real, so not irrational.
• $4i$: Imaginary number, not real, so not irrational.
• $\sqrt{5}$: Cannot be expressed as $\frac{p}{q}$, so it is irrational.
• $5$: Can be written as $\frac{5}{1}$, so it is rational.
• $3+2i$: Complex number (not real), so not irrational.

Answer:

$\sqrt{5}$