Problem 46 - Algebra 2

Question

Evaluate each expression. \(-\sqrt{4}\)

Step-by-Step Solution

Answer

The expression evaluates to -2.

Step 1: Determine the Square Root

To find the square root of 4, recall that the square root of a number is a value that, when multiplied by itself, gives the original number. Since 2 multiplied by 2 is 4, we have \(\sqrt{4} = 2\).

Step 2: Apply the Negative Sign

Now, apply the negative sign in front of the square root. We have \(-\sqrt{4} = -2\). The negative sign indicates the opposite of the positive square root.

Key Concepts

Square Root

When we talk about the square root of a number, we are looking for a value that can be multiplied by itself to give the original number.

• For example, the square root of 4 is 2 because when we multiply 2 by itself, we get 4: \(2 \times 2 = 4\).
• The notation for the square root involves a radical symbol, written as \(\sqrt{...}\).
• Knowing common square roots, like \(\sqrt{4} = 2\) or \(\sqrt{9} = 3\), helps when dealing with more complex expressions.

Some numbers, like 4 or 9, have whole numbers as their square roots. These are known as perfect squares. Understanding that not all square roots are whole numbers lays the groundwork for exploring irrational numbers, which cannot be expressed as simple fractions. Learning about square roots is vital for simplifying and solving equations efficiently.

Evaluating Expressions

Evaluating expressions means finding what the expression equals. Start by simplifying each part of the expression step by step.

• You first deal with operations inside parentheses or radicals.
• After addressing these, you follow the order of operations, remembering the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
• For example, evaluating \(-\sqrt{4}\) means first finding the square root of 4 and then applying the negative sign.

This process ensures that you arrive at the correct answer by addressing the necessary components of the expression in the right order. Breaking down each part and applying foundational math rules makes it easier to evaluate correctly.

Negative Numbers

Negative numbers are numbers less than zero, and they are an essential part of mathematics. They appear often when dealing with subtraction, debts, or temperatures below zero.

• In expressions like \(-\sqrt{4} = -2\), the negative sign indicates the direction or position on the number line, to the left of zero.
• Subtracting a larger number from a smaller one or multiplying a positive by a negative number also results in a negative number.

Handling negative numbers gets easier with practice. Always pay attention to the operation signs in expressions, as they guide you in finding the correct result. Negative signs in expressions must be carefully noted, especially when combining with other negative numbers or signs.