In Exercises 1–12, find each absolute value.
|-√2|
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Understand that the absolute value of a number is its distance from zero on the number line, regardless of direction.
Recognize that the absolute value of a number is always non-negative.
Identify the expression inside the absolute value: .
Since is a negative number, the absolute value will be the positive version of it.
Therefore, the absolute value of is .
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by two vertical bars surrounding the number or expression, such as |x|. For any real number x, the absolute value is defined as |x| = x if x ≥ 0, and |x| = -x if x < 0.
The square root of a number x is a value that, when multiplied by itself, gives x. It is denoted as √x. For positive numbers, there are two square roots: one positive and one negative. However, the principal square root is the non-negative one, which is typically what is referred to when using the square root symbol.
Negative numbers are values less than zero and are represented on the left side of zero on the number line. When calculating the absolute value of a negative number or expression, the result is always positive. For example, |-√2| involves finding the absolute value of a negative square root, which will yield a positive result.