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Chapter 8: Problem 47

Simplify. $$ -16-\sqrt{4} $$

Short Answer

Expert verified
-18

Step by step solution

01

Identify the Expression Components

The expression to simplify is \[-16 - \sqrt{4}\].It consists of the constant number \(-16\) and the square root of \(4\).
02

Simplify the Square Root

Calculate the square root of \(4\). Note that \(\sqrt{4} = 2\) because \(2^2 = 4\).
03

Substitute and Simplify

Substitute \(\sqrt{4}\) with \(2\) in the original expression:\[-16 - 2\].Subtract \(2\) from \(-16\) to get:\[-16 - 2 = -18\].

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Key Concepts

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

Square Roots
Square roots are a fundamental concept in mathematics. They involve finding a number that, when multiplied by itself, equals the original number. For example, the square root of 4 is 2, because 2 multiplied by 2 equals 4.

There are a few key points to remember about square roots:
  • The square root of a perfect square (like 4, 9, 16) is always an integer.
  • Square roots are denoted by the symbol \( \sqrt{} \).
  • Not all numbers have whole number square roots; for instance, \( \sqrt{2} \) is an irrational number.


Understanding how to work with square roots is crucial in simplifying expressions, especially when they appear alongside other numbers or operations. It helps in breaking down complex problems into more manageable parts.
Constants in Algebra
In algebra, constants are fixed values that do not change. Unlike variables, which can represent different numbers, constants have a definite value. Take \(-16\) in the expression \(-16 - \sqrt{4}\). This number remains unchanged as we simplify the expression.

Here are some essential facts about constants:
  • They can be positive, negative, whole numbers, fractions, or decimals.
  • Constants provide a specific value in expressions and equations.
  • When combined with other numbers, they follow the standard arithmetic operations.


By recognizing constants in an expression, you can easily perform arithmetic operations, aiding in simplification and problem-solving.
Step-by-Step Algebra Solutions
Solving algebra problems step-by-step is an effective method to tackle complex expressions. It involves breaking down the problem into smaller, manageable pieces. For the expression \(-16 - \sqrt{4}\), this approach involves identifying components and simplifying each step.

Here's how to approach it:
  • Identify the components: Start by examining the expression. Notice numbers, variables, and operations.
  • Simplify individually: Handle each part separately. In our example, simplify \( \sqrt{4} \) first to get 2.
  • Substitute and perform operations: Replace simplified parts in the expression and carry out the operations, like subtraction.


This structured method helps to avoid mistakes and provides clarity. It ensures that every part of the equation is accurately addressed, leading to correct solutions.

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