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In mathematics, the square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 16 is 4 because 4 times 4 equals 16. The symbol used for square root is \(\sqrt{}\). In the expression \(6 \sqrt{42}\), the number 42 is under the square root symbol, indicating we need to find a number that, when squared, results in 42.

When dealing with square roots, we often encounter both positive and negative roots. However, in most practical cases, we use the positive root only. For example, \(\sqrt{16} = 4\) and \(-4\), but we usually consider \(\sqrt{16} = 4\).

A mathematical expression is a combination of numbers, symbols, and operators (like +, -, *, /) that represent a value. For example, 3 + 2 and 5 * (2 + 1) are both mathematical expressions. These expressions provide instructions on how to perform operations on numbers and variables to achieve a result.

In the given exercise, the expression \(6 \sqrt{42}\) contains a number (6), the square root symbol (\(\sqrt{}\)), and another number (42). This expression represents a specific mathematical calculation—'six times the square root of forty-two.'

Translating mathematical expressions into words helps us understand the operations and relationships between the components better. This process involves identifying each part of the expression and then describing it in natural language.

Number components in a mathematical expression are the individual numbers and symbols that make up the expression. Let's break down the expression \(6 \sqrt{42}\):

• The number 6 is a coefficient, which means it is a constant that multiplies the square root of 42.
• The square root symbol (\(\sqrt{}\)) indicates we need to find the square root of the number inside it.
• The number 42 inside the square root is called the radicand, which is the value we are taking the square root of.

By understanding these components, we can better interpret and solve mathematical expressions. Recognizing that each part of the expression plays a specific role helps simplify complex calculations into more manageable steps.