Problem 67 Find each absolute value. $$|\... [FREE SOLUTION]

Chapter 1: Problem 67

Find each absolute value. $$|\sqrt{2}|$$

Short Answer

Expert verified

$\root{2}$

Step by step solution

Understand the Absolute Value

Absolute value refers to the non-negative value of a number without regard to its sign. The absolute value of a number is always positive or zero.

Identify the Quantity Inside the Absolute Value

Identify the number or expression inside the absolute value bars. In this case, it is $\root{2}$.

Evaluate the Absolute Value

Since $\root{2}$ is already a positive number, the absolute value of $\root{2}$ is $\root{2}$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Non-Negative Value

Numbers can be both positive and negative, but when we talk about their non-negative value, we mean their absolute value. The absolute value represents how far a number is from zero on the number line, ignoring its direction. So, whether a number is positive or negative, its absolute value is always zero or greater. For instance, the absolute value of -5 is 5 because 5 units away from zero is the magnitude we're interested in, not the direction.

Evaluate Absolute Values

To evaluate the absolute value of any number or expression, you simply need to disregard the negative sign, if there is one. Let's go through this step-by-step:

Look at the expression inside the absolute value bars. These bars look like this: $| ... |$.
If the number inside the bars is positive or zero, then the absolute value is the same as that number.
If the number inside the bars is negative, then the absolute value is the same number but without the negative sign.

Using the example: $ |\sqrt{2}| $, $\sqrt{2}$ is already a positive number, so we don't need to change anything. Hence, $ |\sqrt{2}| = \sqrt{2} $.

Positive Numbers

Positive numbers are all the numbers greater than zero. They are found to the right of zero on a number line. They are used in many areas like counting, measurements, and more. When a number is positive, its absolute value is the same as the number itself. For instance, if you have the number 7, its absolute value is also 7 because it's already positive. This is why, when we evaluate $|\sqrt{2}|$, we find that the absolute value is the same as $\sqrt{2}$, since $\sqrt{2}$ is inherently positive.

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91影视

Find each absolute value. $$|\sqrt{2}|$$

Short Answer

Step by step solution

Understand the Absolute Value

Identify the Quantity Inside the Absolute Value

Evaluate the Absolute Value

Key Concepts

Non-Negative Value

Evaluate Absolute Values

Positive Numbers

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