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Chapter 8: Problem 39

Simplify. $$ 81--\sqrt{4} $$

Short Answer

Expert verified
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Step by step solution

01

Simplify the Double Negative

The expression given is \(81 - -\sqrt{4}\). First, simplify the double negative sign. The negative of a negative is positive, so the expression becomes \(81 + \sqrt{4}\).
02

Evaluate the Square Root

Calculate the square root of 4. Since \(\sqrt{4} = 2\), substitute this value into the expression to get \(81 + 2\).
03

Add the Values

Finally, add 81 and 2 together. \(81 + 2 = 83\).

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Key Concepts

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

Double Negative
A double negative occurs in math expressions when two negative signs are placed together. Just like in language, where two negatives make a positive statement, in mathematics, a double negative turns into a positive.
Consider the expression given in the problem: \(81 - -\sqrt{4}\). Here, "- -" is an example of a double negative. Simplifying this involves transforming those double negatives into a single positive:
  • Remove the double negative, changing \(- -\) to \(+\).
  • The expression then becomes \(81 + \sqrt{4}\).
This process can be very handy during algebraic manipulations and helps to avoid errors in calculations!
Square Root
The square root is a concept in mathematics used to find a number that, when multiplied by itself, gives the original number. In simpler terms, it's the opposite of squaring a number.
For example, the square root of 4 is written as \(\sqrt{4}\). To determine this, ask yourself: "What number multiplied by itself equals 4?" The answer is 2, because \(2 \times 2 = 4\).
  • To simplify \(\sqrt{4}\), write it as 2 because \(\sqrt{4} = 2\).
  • Now replace \(\sqrt{4}\) in the expression \(81 + \sqrt{4}\) with 2, getting \(81 + 2\).
Understanding square roots is fundamental for solving many math problems, especially those involving radicals.
Arithmetic Operations
Arithmetic operations are the basic math calculations we perform nearly every day. They include addition, subtraction, multiplication, and division.
In the context of our exercise, we focus on addition: combining numbers to get a total. Once we simplified the expression to \(81 + 2\), the final step is to complete the addition:
  • Add 81 and 2 together, which equals 83.
These operations form the foundation of almost all math calculations. With practice, they become automatic processes in your problem-solving toolkit!

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