Problem 22 - Algebra 1: Concepts and Skills

Question

Write the equation in words. $$ \sqrt{49}=7 $$

Step-by-Step Solution

Answer

The square root of forty-nine equals seven.

Step 1: Identify the Main Components

Break the equation into parts, identifying the main components which in this case are: the square root sign, the number '49' inside the square root, the equals sign, and the number '7'.

Step 2: Convert the Components Into Words

The square root sign represents the operation of finding the square root. The number '49' will just be pronounced as 'forty-nine'. The equals sign can be converted to 'is equal to' or 'equals'. The number '7' will be pronounced as 'seven'.

Step 3: Combine the Words to Form the Equation

By reassembling these parts, the equation can be written in words as: 'The square root of forty-nine equals seven'.

Step 4: Proofread

Confirm that the sentence you have written makes sense in the context of the original equation and that all components have been accurately transferred into words.

Key Concepts

Square Root

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, in the equation \( \sqrt{49} = 7 \), the square root of 49 is 7. This is because when 7 is multiplied by itself (7 x 7), the result is 49.

Understanding square roots is essential for various mathematical applications and solving quadratic equations. It is also the basis for understanding more complex concepts in algebra and geometry. When you encounter a square root sign, always think of it as a question: what number times itself will give me the number under the square root sign?

Equation Translation

Translating an equation into words is an important skill in mathematics that helps to ensure understanding of the underlying concepts. It involves describing mathematical symbols and numbers in plain language. In the equation \( \sqrt{49} = 7 \), it translates to 'The square root of forty-nine equals seven.'

This translation communicates not just the mathematical operation, but also establishes a relationship between numbers. Learning to translate equations can also aid in verbalizing problem-solving strategies, which is a crucial part of learning mathematics and mathematical reasoning.

Mathematical Terminology

Key Terms

Mathematical terminology provides the words we need to describe mathematical concepts succinctly and precisely. In our example, terms like 'square root' and 'equals' have specific meanings. The square root is the inverse operation of squaring. 'Equals' signifies equivalence or equality between the expressions on either side of the equation.

Developing a good grasp of mathematical terminology is vital because it allows students to communicate ideas accurately, understand instructions, and follow mathematical reasoning more effectively.

Algebraic Concepts

Basic Algebraic Operations

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols to solve problems. The equation \( \sqrt{49} = 7 \) is an example of an algebraic concept, where the square root operation is used to find an unknown quantity. Here, the concept of equality (\