key term - Radicand

Definition

The radicand is the number or expression under the radical sign in a square root or higher root expression. It is the quantity that is being operated on by the root function.

5 Must Know Facts For Your Next Test

1. The radicand determines the value of the square root or higher root expression.
2. Simplifying a square root involves finding the largest perfect square factor of the radicand.
3. Adding or subtracting square roots requires that the radicands be like terms (have the same value inside the radical).
4. Multiplying square roots involves multiplying the radicands together.
5. Dividing square roots involves dividing the radicands.

Review Questions

• Explain how the radicand is used in the context of simplifying square roots.
  • When simplifying a square root, the goal is to find the largest perfect square factor of the radicand and extract it from the radical. This is done by factoring the radicand and identifying the largest perfect square factor. For example, to simplify $\sqrt{72}$, the radicand is 72, and the largest perfect square factor is 4, so the simplified expression is $2\sqrt{18}$.
• Describe the role of the radicand when adding or subtracting square roots.
  • When adding or subtracting square roots, the radicands must be like terms, meaning they have the same value inside the radical. For example, $\sqrt{16} + \sqrt{9}$ can be simplified to $4 + 3 = 7$, because the radicands 16 and 9 are both perfect squares. However, $\sqrt{16} + \sqrt{18}$ cannot be simplified further because the radicands are not like terms.
• Analyze how the radicand is used when multiplying or dividing square roots.
  • When multiplying square roots, the radicands are multiplied together. For example, $\sqrt{4} \cdot \sqrt{9} = \sqrt{36} = 6$. When dividing square roots, the radicands are divided. For example, $\frac{\sqrt{36}}{\sqrt{9}} = \frac{6}{3} = 2$. In both cases, the radicand is the key factor that determines the result of the operation.

Related terms

Radical:

A radical is the symbol (√) used to indicate a root operation, such as a square root or cube root.

Perfect Square:

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

Rational Exponent: A rational exponent is an exponent that can be expressed as a fraction, such as 1/2 or 3/4, which correspond to square roots and cube roots, respectively.