Problem 669 Simplify. $$ -\sqrt{1} $$... [FREE SOLUTION]

Chapter 1: Problem 669

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

Short Answer

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-1

Step by step solution

Understand the Square Root

The square root of a number is a value that, when multiplied by itself, gives that number. For instance, $\sqrt{1} = 1$ because $1 \times 1 = 1$.

Apply the Square Root

Calculate the square root of 1. From the previous definition, $\sqrt{1} = 1$.

Consider the Negative Sign

The expression given has a negative sign in front of the square root. Therefore, we need to multiply the result from Step 2 by -1. $-\sqrt{1} = -1$.

Simplify the Expression

Combining what we have up to this point, the simplified form of the expression $-\sqrt{1}$ is $-1$.

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Key Concepts

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

Square Root

Understanding the concept of a square root is crucial for many mathematical problems. The square root of a number is a value that, when multiplied by itself, returns the original number. For example, the square root of 9 is 3, because $3 \times 3 = 9$. Similarly, $ \sqrt{4} = 2$ since $2 \times 2 = 4$.
Square roots are represented by the symbol $ \sqrt{} $ and can be applied to both positive and negative numbers. However, for real numbers, the square root is generally considered only for non-negative numbers.

Negative Numbers

Negative numbers represent values less than zero and are denoted with a minus sign (-). In the context of our exercise, understanding how to handle negative signs is important. For example, if you have the expression $- \sqrt{4} $, you first calculate the square root of 4, which is 2, and then apply the negative sign to get -2.
Negative numbers can change the result of an expression significantly, so always pay close attention to them. When simplifying expressions involving square roots and negative signs, perform each operation step-by-step to avoid mistakes. This is exactly what we did in the exercise when we calculated $ - \sqrt{1} $ to get -1.

Basic Algebra

Basic algebra involves understanding and manipulating mathematical symbols according to certain rules. In the exercise, we used algebraic principles to simplify the expression $ - \sqrt{1} $. First, we identified the square root, then applied it, and finally, we multiplied the result by -1.
Algebra often involves combining like terms, performing operations according to the order of operations (PEMDAS鈥擯arentheses, Exponents, Multiplication and Division, Addition and Subtraction), and understanding how to work with variables and constants. These principles are key to solving more complex mathematical equations and understanding higher-level math concepts.

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91影视

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

Short Answer

Step by step solution

Understand the Square Root

Apply the Square Root

Consider the Negative Sign

Simplify the Expression

Key Concepts

Square Root

Negative Numbers

Basic Algebra

One App. One Place for Learning.

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