Problem 21 - Algebra 1: Concepts and Skills

Question

Write the equation in words. $$ -\sqrt{289}=-17 $$

Step-by-Step Solution

Answer

The negative square root of two hundred eighty-nine is negative seventeen.

Step 1: Identify the Parts of the Equation

The given equation is \( -\sqrt{289} = -17 \). This equation has three main parts: the negative square root symbol \( -\sqrt{} \), the number 289 which is inside the square root, and the number -17 which is the result of the operation.

Step 2: Translate Mathematical Symbols into Words

The negative square root symbol \( -\sqrt{} \) can be translated into words as 'the negative square root of'. The equals sign \( = \) is simply translated to 'is' or 'equals'.

Step 3: Write the Equation in Words

Now using the translations from step 2, the equation can be written in words as follows: 'The negative square root of two hundred eighty-nine is negative seventeen'.

Key Concepts

Mathematical Symbols in Words

Mathematical symbols are like a special language. They allow us to write complex ideas quickly and precisely. Understanding how to translate these symbols into words is important for grasping math concepts. For example, the negative square root symbol, \( -\sqrt{} \), indicates that we are looking for the negative value of a number that when multiplied by itself gives the original number inside the root. The equals sign \( = \) is one of the simplest, yet most powerful symbols, showing a balance between two mathematical expressions. When translated into words, it becomes 'is' or 'equals'. These translations are crucial for all students as they transform abstract symbols into understandable phrases.

Square Root in Words

The square root of a number is a value that, when multiplied by itself, returns the original number. For instance, the square root of 289 is 17, because 17 multiplied by 17 equals 289. When writing equations that include a square root, like \( \sqrt{} \), in words, we refer to it simply as 'the square root of'. If the square root symbol includes a negative sign, \( -\sqrt{} \), we add 'negative' in front, making it 'the negative square root of'. This helps differentiate solutions since every positive number actually has both a positive and a negative square root.

Negative Numbers in Equations

Understanding negative numbers is fundamental in mathematics. A negative number is any number less than zero, represented with a minus sign (\(-\)). In equations, such as \( -\sqrt{289}=-17 \), the negative sign indicates that the number or operation following it is the opposite of a positive number. Negative numbers in equations can represent several real-world scenarios, like debt in finance or a decrease in temperature. When dealing with equations, recognizing the role and meaning of negative numbers ensures clarity in the interpretation of results.

Interpreting Mathematical Equations

Interpreting mathematical equations involves translating them into understandable language, identifying their components, and understanding their implications. Taking \( -\sqrt{289} = -17 \) as an example, we start by breaking down the formula: the negative square root of 289 is translated to 'negative seventeen'.

• The expression \( -\sqrt{289} \) suggests finding the value which when multiplied by itself gives 289, but in its negative form.
• The equals symbol \( = \) shows equivalence, meaning both sides represent the same quantity.
• Finally, recognizing \( -17 \) as the result confirms understanding.

This comprehension process not only aids in solving equations but also in applying mathematical concepts to real-life situations, promoting deeper learning.