Problem 19 - Algebra 1: Concepts and Skills

Question

Write the equation in words. $$ \sqrt{225}=15 $$

Step-by-Step Solution

Answer

the square root of two hundred twenty-five is equal to fifteen

Step 1: Identify Mathematical Operations and Symbols

Start by identifying each component of the provided equation. This includes: the square root symbol, the equal sign, and the numbers 225 and 15.

Step 2: Transcribe Square Root Operation

The square root of 225 is written as 'the square root of two hundred and twenty-five'.

Step 3: Transcribe Equals Sign

The equal sign is read or written as 'is equal to' in this context.

Step 4: Transcribe Number 15

The number 15 is written as 'fifteen'.

Step 5: Combine Components

Now, put all the identified and transcribed components together in the correct order: 'The square root of two hundred twenty-five is equal to fifteen'.

Key Concepts

Square Root Operation

Understanding the square root operation is fundamental in mathematics. Simply put, finding the square root of a number means identifying a value that, when multiplied by itself, equals the original number. For example, the square root of 225 is written mathematically as \( \sqrt{225} \). This expression reads as 'the square root of two hundred twenty-five'.

Here's a closer look at the process:

• The square root symbol (\( \sqrt{} \)) signifies the operation.
• The number inside the square root, in this case, 225, is known as the radicand.
• The result of this operation, here number 15, means that \( 15 \times 15 = 225 \).

Understanding this operation is crucial because it is a building block for more advanced mathematical concepts such as solving quadratic equations and understanding irrational numbers.

Mathematical Notation

Mathematical notation is the system of symbols and signs used to write equations and express mathematical thoughts. It's the language mathematics speaks. Getting familiar with this language can significantly ease understanding and communication of mathematical ideas.

Consider the equation \( \sqrt{225}=15 \), each part of it is symbolic:

• The square root symbol (\( \sqrt{} \)) indicates a specific operation to be performed on the number that follows.
• The equal sign (\( = \)) denotes that the value on the left side of the equation is identical to the value on the right.
• Numbers like 225 and 15 are operands, and they are subject to the operations denoted by the symbols around them.

The precise and concise nature of mathematical notation is what makes it effective for conveying complex ideas succinctly. Sometimes, however, it is important to write these symbols in words to ensure clarity, especially for those who are just beginning to learn this 'language'.

Verbalizing Math Equations

Verbalizing math equations is the skill of expressing mathematical symbols and operations in words. It is an essential part of mathematics education because it bridges the gap between abstract equations and comprehension.

When verbalizing the equation \( \sqrt{225}=15 \), the steps include identifying and articulating each component:

1. Start with the square root symbol. It is verbalized as 'the square root of'.
2. Then, mention the radicand, in our case, 225, which is said as 'two hundred twenty-five'.
3. The equal sign translates to 'is equal to'.
4. Finally, state the result, which here is the number 15, spoken as 'fifteen'.

By verbalizing the equation, 'The square root of two hundred twenty-five is equal to fifteen,' we convert the language of mathematics into spoken word, enhancing understanding and making it more accessible, especially for learners who are visual or auditory.