Drag each expression into the correct category.

Question

Response area with 2 blank spaces
Result is a Rational Number

Blank space 1 empty


Result is an Irrational Number
Blank space 3 empty


Answer options with 8 options.

Answer 1

To categorize expressions as either resulting in a rational number or an irrational number, here’s a general guideline:

Rational Numbers:

1. Integers: Any whole number (positive, negative, or zero) is rational. e.g., -3, 0, 4
2. Fractions: Any number that can be expressed as the quotient of two integers, where the denominator is not zero. e.g., 1/2, -3/4
3. Repeating or terminating decimals: Numbers like 0.75, 1.333..., etc.

Irrational Numbers:

1. Non-repeating, non-terminating decimals: Numbers that cannot be expressed as a fraction. e.g., √2, π
2. Roots of non-perfect squares: Like √3, √5, etc. (that cannot be simplified to a whole number)
3. Certain mathematical constants: Such as e, π, and others that do not terminate or repeat.

Missing Expressions:

Without the specific expressions to categorize, I cannot place them into correct spaces. However, you can use the guidelines above to categorize them based on whether they meet the criteria of rational or irrational.

If you have specific expressions, please provide them, and I can help categorize them accordingly!