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Chapter 9: Problem 9

Simplify. $$ \sqrt{529} $$

Short Answer

Expert verified
The simplified form of \sqrt{529} is 23.

Step by step solution

01

Understand the Problem

The task is to simplify the square root of 529. Simplifying the square root involves finding a number that, when multiplied by itself, gives the original number.
02

Identify Perfect Squares

Look for perfect squares that might be close to or equal to 529. Perfect squares are numbers like 1, 4, 9, 16, 25, etc.
03

Calculate the Square Root

Check if 529 is a perfect square by calculating its square root. Use a calculator or factors to determine that \(23 \times 23 = 529\).
04

Simplify

Since \(23 \times 23 = 529\), the square root of 529 is 23. Therefore, \(\forall a \in \{ x | \sqrt{x} = \sqrt{529} \}\), that means \ \forall x \in 23.

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Key Concepts

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

perfect squares
Perfect squares are numbers that can be expressed as the product of an integer with itself. For example, 1 can be written as 1 脳 1, 4 as 2 脳 2, 9 as 3 脳 3, and so on.
These numbers are essential in simplifying square roots because they help us identify whether a given number is a perfect square.
In the exercise, 529 is identified as a perfect square. By knowing this, we could directly jump to the conclusion that its square root is an integer.
square root calculation
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, \(\text{鈭�16 = 4}\).
Calculating the square root involves determining which number, when squared, makes the original number.
You can find the square root by various methods, such as:
  • Prime factorization
  • Using a calculator
  • Estimation and refinement
For the exercise with 529, we observed that \(\text{23 脳 23 = 529}\), thus \(\text{鈭�529 = 23}\).
mathematics education
Grasping fundamental concepts like perfect squares and square root calculations is vital in mathematics education. These concepts lay the groundwork for more advanced topics.
Here are a few tips to make grasping them easier:
  • Use visual aids like number lines or area models to illustrate square roots and perfect squares.
  • Solve various problems to gain confidence in identifying and working with perfect squares.
  • Practice regularly with real-world examples to make the concepts relatable.
The more you practice and relate mathematical concepts to everyday situations, the more understandable and less intimidating they become.

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