Problem 349 - Prealgebra

Question

Translate from math notation to words. $$7 \sqrt{63}$$

Step-by-Step Solution

Answer

Seven times the square root of sixty-three.

Step 1: Identify the Expression

The given mathematical expression is \(7 \sqrt{63}\).

Step 2: Understand the Components

The expression consists of two parts: the coefficient '7' and the square root of '63'.

Step 3: Translate the Coefficient

The number '7' is written as 'seven' in words.

Step 4: Translate the Radical

The square root symbol (\(\sqrt{}\)) means 'the square root of'. The number '63' follows this symbol.

Step 5: Combine the Translations

Combine the translations of the coefficient and the radical. The entire expression \(7 \sqrt{63}\) translates to 'seven times the square root of sixty-three'.

Key Concepts

square root

A square root is a special mathematical symbol that helps you find a number which, when multiplied by itself, gives back the original number under the square root.
It is represented by the radical symbol \(\sqrt{}\). For instance, if we look at \(\sqrt{9}\), we are asked to find a number which, when multiplied by itself, equals 9. In this case, it's 3, because 3 * 3 = 9.
Let's break down how to understand the square root symbol further:

• It's like asking, 'What number squared equals this number?'
• Think of it as undoing a multiplication.

In our original exercise, \(\sqrt{63}\) asks, 'What number, when squared, equals 63?' While 63 is not a perfect square, this shows how closely related the concept is to multiplication.

coefficient

The term 'coefficient' might sound fancy, but it just refers to the number placed in front of variables or other items in mathematical expressions.
In our exercise, the coefficient is 7 in \(7 \sqrt{63}\). This means that 7 times the value of the square root of 63 is considered.
Coefficients are important because they scale the value of the entire expression.

• They can be any number, positive or negative.
• They might also be in decimals or fractions.

Understanding this allows you to interpret the size and effect of different parts in mathematical expressions.

mathematical expression

A mathematical expression is a combination of numbers, variables, and operations like addition, multiplication, or taking square roots.
Expressions can include complex combinations of terms, but can also be as simple as a single number.
In the example \(7 \sqrt{63}\), we have a combination of a coefficient (7) and a square root operation applied to 63.

• They don't always have an equal sign, and if they do, they become 'equations'.
• Knowing how to read them and translate them into words can simplify solving or understanding their meaning.

Breaking down an expression into its components, like separating the 7 from the square root of 63, makes it easier to translate and understand.