What type of number is -√16? Choose all answers that apply.
Understand the Problem
The question is asking to identify the type of number that is represented by the expression -√16. It is necessary to evaluate the expression first, then classify the result according to the provided categories.
Answer
Integer and Rational.
Answer for screen readers
The types of numbers that -√16 represents are Integer and Rational.
Steps to Solve
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Evaluate the Square Root First, we need to evaluate the expression $-\sqrt{16}$. The square root of 16 is 4, so we have: $$ -\sqrt{16} = -4 $$
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Classify the Result Now we need to classify the result, which is -4.
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Whole Number: Whole numbers are non-negative integers (0, 1, 2, ...). Since -4 is negative, it is not a whole number.
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Integer: Integers include all whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3, ...). Since -4 is an integer, it qualifies.
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Rational Number: Rational numbers are numbers that can be expressed as the ratio of two integers (for example, $-\frac{4}{1}$). Since -4 can be expressed in this way, it is a rational number.
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Irrational Number: Irrational numbers cannot be expressed as the ratio of two integers (like $\sqrt{2}$ or $\pi$). Since -4 can be expressed as a ratio, it is not an irrational number.
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Consolidate the Classifications Based on our classifications:
- Whole number: No
- Integer: Yes
- Rational: Yes
- Irrational: No
The types of numbers that -√16 represents are Integer and Rational.
More Information
- The square root of a perfect square (like 16) yields a whole number.
- The negative of this whole number is classified within integers and rational numbers due to how they are defined.
Tips
- A common mistake is to classify negative numbers as whole numbers; remember whole numbers cannot be negative.
- Confusing rational and irrational numbers can also occur; always check if the number can be expressed as a fraction.
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