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Chapter 9: Problem 15

In Exercises \(11-18,\) Ind the geometric mean of the two numbers. 16 and 25

Short Answer

Expert verified
Therefore, the geometric mean of the numbers 16 and 25 is 20.

Step by step solution

01

Identify Given Numbers

Recognize the provided numbers, which are 16 and 25.
02

Calculate Product

Multiply the given numbers together. The multiplication of 16 and 25 equals to 400.
03

Find Geometric Mean

Find the square root of the product. The square root of 400 is 20.

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Key Concepts

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

Square Root
The square root is a fundamental concept in mathematics that refers to a number which, when multiplied by itself, results in a given number. For example, the square root of 400 is 20 because 20 multiplied by 20 equals 400.

To find the square root, you often look for a number that is exact, or in some cases, you might need a calculator or solve an equation manually.

Understanding square roots can help in various real-world situations, such as finding dimensions in geometry or working with formulas in physics and algebra.
Multiplication
Multiplication is an arithmetic operation used for finding the total number of objects in a group when you have a certain number of equal groups. It鈥檚 often described as repeated addition. For example, adding 16 twenty-five times is the same as multiplying 16 by 25.

When learning multiplication, it is important to remember:
  • The numbers being multiplied are called factors.
  • The result of multiplication is called the product.

In the given exercise, multiplying the numbers 16 and 25 gives us 400. Mastery of multiplication is crucial, as it forms a basis for more complex mathematical operations and is used daily in real-life scenarios, such as calculating costs or quantities.
Mathematics Education
Mathematics education is the discipline of teaching and learning mathematics. It's more than just numbers; it鈥檚 about developing problem-solving skills and logical thinking.

In mathematics education, a strong foundation in basic operations such as multiplication and understanding concepts like square roots is essential. This foundation helps in grasping more complex ideas later on.

The goal is to make mathematics accessible, approachable, and applicable to everyday life. Engaging methods, like interactive exercises and real-world applications, enhance the learning experience, making students more confident and skilled in tackling mathematical problems.

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