key term - ∜

Definition

The symbol ∜ is known as the radical symbol or square root symbol. It represents the operation of finding the square root of a number or expression. The square root of a number is the value that, when multiplied by itself, results in the original number.

5 Must Know Facts For Your Next Test

1. The square root symbol ∜ is used to represent the operation of finding the square root of a number or expression.
2. When dividing radical expressions, the ∜ symbol is used to indicate that the division is being performed on the square roots of the expressions.
3. Simplifying radical expressions involves rewriting them in a form where the radicand is as small as possible, often by factoring out perfect squares.
4. Rationalizing the denominator of a fraction with a radical expression involves multiplying the numerator and denominator by a value that will eliminate the radical in the denominator.
5. The properties of square roots, such as $∜(a \cdot b) = ∜a \cdot ∜b$ and $∜(a/b) = ∜a / ∜b$, are important when dividing radical expressions.

Review Questions

• Explain how the square root symbol ∜ is used in the context of dividing radical expressions.
  • When dividing radical expressions, the square root symbol ∜ is used to indicate that the division is being performed on the square roots of the expressions. For example, to divide $∜24$ by $∜6$, the division can be rewritten as $∜24 / ∜6$. This allows for the application of the property $∜(a/b) = ∜a / ∜b$, which simplifies the expression to $∜4$. The ∜ symbol is crucial in maintaining the correct mathematical operations when dividing radical expressions.
• Describe the process of simplifying a radical expression and how it relates to the square root symbol ∜.
  • Simplifying a radical expression involves rewriting it in a form where the radicand (the number under the square root symbol) is as small as possible. This is often done by factoring out perfect squares from the radicand. For example, to simplify $∜48$, we can factor out the perfect square 16, resulting in $∜48 = ∜(16 \cdot 3) = ∜16 \cdot ∜3 = 4∜3$. The square root symbol ∜ is essential in this process, as it allows us to isolate the square root of the perfect square and the remaining radicand.
• Analyze the properties of square roots and explain how they are applied when dividing radical expressions.
  • The properties of square roots, such as $∜(a \cdot b) = ∜a \cdot ∜b$ and $∜(a/b) = ∜a / ∜b$, are crucial when dividing radical expressions. These properties allow us to manipulate the square root symbol ∜ to simplify the division process. For example, to divide $∜24$ by $∜6$, we can apply the property $∜(a/b) = ∜a / ∜b$ to rewrite the expression as $∜24 / ∜6$, which simplifies to $∜4$. Understanding and applying these square root properties, in conjunction with the square root symbol ∜, is essential for effectively dividing radical expressions.

Related terms

Radical Expression:

A radical expression is a mathematical expression that contains one or more square roots.

Radicand:

The radicand is the number or expression under the radical symbol, which is the value whose square root is being found.

Perfect Square:

A perfect square is a number that can be expressed as the product of two equal integers, such as 4 (2 x 2), 9 (3 x 3), or 16 (4 x 4).