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Chapter 0: Problem 83

Simplify each expression. \(\sqrt{100}\)

Short Answer

Expert verified
The simplified form of \(\sqrt{100}\) is 10.

Step by step solution

01

Identify the Square Root

Recognize that the problem is asking for the square root of 100, which means we need to find a number that, when multiplied by itself, gives 100.
02

Find the Number

Determine which number squared equals 100. Since \(10 \times 10 = 100\), the number is 10.
03

Simplify

Since \(10 \times 10 = 100\), we write \(\sqrt{100} = 10\). Therefore, the simplified form of \(\u200B\root 100\) is 10.

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Key Concepts

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

Simplifying expressions
Simplifying expressions is a fundamental skill in algebra. It involves rewriting an expression in its simplest form.
This often includes combining like terms, reducing fractions, and performing arithmetic operations.
By doing this, we make the expression easier to work with and understand.
For example, in the exercise where we simplified \(\root{}100\), we ultimately find the simplest form of this expression.
This entails recognizing that \(\root{}100\) equals 10. Understanding how to simplify expressions can make complex problems more manageable and solve them efficiently.
Square root calculation
Calculating the square root of a number means finding another number which, when multiplied by itself, equals the original number.
The symbol for the square root is \(\root{}\).
In our example, \(\root{}100\), we looked for a number that, when squared, gives 100. This number is 10.
To simplify this calculation, it's helpful to know the squares of smaller numbers:
  • \(\root{}1\) = 1
  • \(\root{}4\) = 2
  • \(\root{}9\) = 3
  • \(\root{}16\) = 4
  • \(\root{}25\) = 5
In practice, repeatedly developing familiarity with such calculations builds confidence and speed in simplifying more complex expressions.
Basic algebra
Basic algebra is the branch of mathematics dealing with symbols and the rules for manipulating those symbols.
It's about understanding how to solve equations and perform operations.
One key aspect of algebra is working with square roots and simplifying expressions, just like we did in our exercise.
Here are some fundamental concepts of basic algebra:
  • Variables: Symbols used to represent unknown values (e.g., x, y).
  • Constants: Fixed values (e.g., numbers like 5, -3).
  • Equations: Mathematical statements indicating that two expressions are equal (e.g., \(2x + 3 = 7\)).
Mastering these basics is essential for tackling more advanced topics in mathematics effectively.

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Most popular questions from this chapter

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