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Chapter 9: Problem 11

Simplify. $$ -\sqrt{1} $$

Short Answer

Expert verified
-1

Step by step solution

01

Evaluate the Square Root

Find the square root of the number inside the radical. In this case, the square root of 1. The square root of 1 is 1 since \[1^2 = 1.\]
02

Apply the Negative Sign

Apply the negative sign in front of the square root. Since the radical expression \(-\sqrt{1}\) has a negative sign, multiply the result from Step 1 by -1: \(-1\).
03

Simplified Result

Combine the results from Step 1 and Step 2. The simplified form of \(-\sqrt{1}\) is \(-1\).

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Key Concepts

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

Evaluating Square Roots
Understanding how to evaluate square roots is key to many algebraic operations. The square root of a number is a value that, when multiplied by itself, gives the original number.
For instance, the square root of 1, denoted as \(\text{鈭�1}\) \, is 1. Why? Because when you square 1 - that is, multiply 1 by itself - you get 1: \[ 1^2 = 1 \]
Remember, some numbers do not have a neat square root, but we can often approximate them to simplify our calculations.
However, for numbers like 1, which are perfect squares, finding the square root is straightforward.
Negative Sign Application
Let's talk about the negative sign in front of the square root. Applying a negative sign to the square root of a number means you are effectively multiplying the square root by -1.
Take the example \(\text{-鈭�1}\)\, where the square root of 1 is evaluated first (which is 1). Then, you multiply this result by -1: \[ -1 \times 1 = -1 \]
It's essential to remember that this negative sign does not affect the calculation inside the square root - it only affects the final result after you have evaluated the square root.
Simplifying Expressions
Simplifying expressions involving square roots and negative signs is a step-by-step process.
To simplify the expression \(\text{-鈭�1}\)\, we first find the square root of the number inside the radical (which is 1). Second, we apply the negative sign to this result.
So the simplified form of \(\text{-鈭�1}\)\ is simply \(-1\). Breaking it into steps helps ensure we do not miss any part of the process.
In general, simplifying expressions means breaking them down into their simplest forms where no further reduction is possible, making the calculations easier and more manageable.

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Most popular questions from this chapter

In the following exercises, simplify by rationalizing the denominator. $$ \frac{\sqrt{150 x^{2} y^{6}}}{\sqrt{6 x^{4} y^{2}}} $$

In the following exercises, simplify. $$ \frac{\sqrt{26 y^{7}}}{\sqrt{2 y}} $$

In the following exercises, simplify and rationalize the denominator. $$ \frac{4}{\sqrt{5}} $$

In the following exercises, simplify and rationalize the denominator. $$ \sqrt{\frac{4}{27}} $$

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