The radicand is the number or expression inside a radical symbol. For example, in $$\text{√}12$$ , 12 is the radicand.

How do you simplify $$\text{√}12$$ ?

$$\text{√}12 = \text{√}(4 \times 3) = \text{√}4 \times \text{√}3 = 2\text{√}3$$ .

Simplify $$\frac{8}{\text{√}6}$$ .

$$\frac{8}{\text{√}6} \times \frac{\text{√}6}{\text{√}6} = \frac{8\text{√}6}{6} = \frac{4\text{√}6}{3}$$ .

What is the simplified form of $$\frac{10}{\text{√}12}$$ ?

$$\frac{10}{\text{√}12} \times \frac{\text{√}12}{\text{√}12} = \frac{10\text{√}12}{12} = \frac{5\text{√}3}{3}$$ .

Why is $$\frac{1}{\text{√}x}$$ not in simplified form?

Because it has a radical in the denominator. It can be simplified by multiplying by $$\frac{\text{√}x}{\text{√}x}$$ .

What is the first step in simplifying a radical expression?

Identify and factor out any perfect square factors from the radicand.

What does it mean if a radical expression is in simplest form?

A radical expression is in simplest form if there are no perfect square factors in the radicand other than 1, and there are no radicals in the denominator.

How do you determine if $$\text{√}x$$ is simplified?

Check if the radicand x has any perfect square factors other than 1. If it does, it can be simplified further.

What is the simplified form of $$\text{√}18$$ ?

$$\text{√}18 = \text{√}(9 \times 2) = \text{√}9 \times \text{√}2 = 3\text{√}2$$ .

What is the significance of simplifying radical expressions?

Simplifying radical expressions makes them easier to work with in calculations and helps in solving equations.

Provide an example of a radical expression that is not simplified.

$$\text{√}8$$ is not simplified because it can be expressed as $$2\text{√}2$$ .

Radicals & Simplifying Radical Expression Flashcards

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