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Chapter 10: Problem 3

Evaluate or simplify each expression. (Assume \(x \geq 0 .)\) $$-\sqrt{4}$$

Short Answer

Expert verified
The value is \(-2\).

Step by step solution

01

Identify the square root

First, identify the square root component within the expression. The given expression is \(-\sqrt{4}\). Here, we need to find the square root of 4.
02

Calculate the square root

Calculate the square root of 4. Recall that \(\text{if } x = 0, 4 = x^2 \text{ then } x\text{ must equal } 2\). Therefore, \(\text{the square root of 4 is 2}\).
03

Apply the negative sign

Next, apply the negative sign that is outside the square root. Thus, \(-\sqrt{4} = -2\).

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Key Concepts

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

Evaluating Expressions
Evaluating expressions involves finding the value of the variable or constants that make up an equation or an expression. It鈥檚 a fundamental skill in mathematics. To evaluate the expression correctly, follow these steps:
  • Identify all parts of the expression, including operations such as addition, subtraction, multiplication, and division.

  • Compute any square roots, powers, or other functions as necessary. For instance, with \[-\sqrt{4}\], you need to first determine the square root of 4, which is 2.

  • Apply any remaining operations, such as the negative sign in our example. This results in \[-\sqrt{4} = -2\].

Practicing these steps will help you evaluate more complex expressions with confidence!
Simplifying Expressions
Simplifying expressions means reducing them to their simplest form. This can involve a variety of steps, such as combining like terms and applying arithmetic operations. Here鈥檚 how to simplify:
  • Break down the expression into individual components.

  • Identify and combine any like terms. For example, with \[-\sqrt{4}\], the expression is already simple. The only operation needed is finding the square root.

  • Perform any calculations necessary. Calculate \sqrt{4}\ to get 2.

  • Apply any final operations, in this case, the negative sign, to get \-2\.

Always double-check your work to ensure your expression is as simple as possible!
Negative Numbers
Negative numbers represent values less than zero and are often encountered in mathematics when working with various expressions and equations. Here鈥檚 what to remember:
  • Negative numbers are denoted by a minus sign in front of the number, such as -2.

  • When applying operations, keep the negative sign consistent. If the expression is \[-\sqrt{4}\], solve the square root first to get 2, then apply the negative sign to get -2.

  • Understanding how to handle negative numbers is crucial for evaluating and simplifying expressions correctly. They follow specific rules for arithmetic operations, such as \[-2 \times 3 = -6\] and \[2 - 5 = -3\].

Practice with different scenarios to get comfortable with negative numbers and their operations.

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Most popular questions from this chapter

Factor the given expression as completely as possible. $$2 x^{2}-50$$

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$\sqrt{12}+\sqrt{27}$$

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$4 \sqrt{96}-5 \sqrt{24}$$

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$b^{2} \sqrt{40 a^{5} b^{2}}+a \sqrt{90 a^{3} b^{6}}$$

Estimate the given square root between two consecutive integers without using a calculator, then use a calculator to find the square root rounded to two decimal places to confirm your estimate. $$\sqrt{872}$$
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