A radical is a symbol that represents the root of a number, most commonly the square root. For example, $$\text{the square root of } 9 \text{ is represented as } \\sqrt{9} = 3$$ .

How do you simplify $$\text{the radical } \\sqrt{72}?$$

$$\text{To simplify } \\sqrt{72}, \text{ factor it as } \\sqrt{36 \times 2} = \\sqrt{36} \times \\sqrt{2} = 6\\sqrt{2}$$ .

What is the simplified form of $$\text{the radical } \\sqrt{20a^2b^4}?$$

$$\text{The simplified form is } 2ab^2\\sqrt{5}$$ .

How do you simplify $$\text{the radical } \\sqrt{200}?$$

$$\text{To simplify } \\sqrt{200}, \text{ factor it as } \\sqrt{100 \times 2} = \\sqrt{100} \times \\sqrt{2} = 10\\sqrt{2}$$ .

What is a perfect square?

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

How do you identify perfect square factors of a number?

To identify perfect square factors, list the factors of the number and check which of them are perfect squares. For example, for 72, the perfect square factors are 1, 4, and 36.

What is the simplified form of $$\text{the radical } \\sqrt{50}?$$

$$\text{The simplified form is } 5\\sqrt{2}$$ .

What is the process of simplifying radicals with variables?

To simplify radicals with variables, apply the same rules as with numbers. For example, $$\text{in } \\sqrt{a^2} = a$$ .

What is the significance of the index in a radical?

The index indicates the degree of the root. For example, in $$\text{the radical } \\sqrt[3]{8}$$ , the index is 3, meaning it is the cube root.

How do you combine radicals?

You can combine radicals by adding or subtracting them if they have the same radicand. For example, $$\text{ } \\sqrt{2} + 3\\sqrt{2} = 4\\sqrt{2}$$ .

What is the difference between rational and irrational numbers?

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction. The square root of a non-perfect square is an example of an irrational number.

Simplifying Radicals Flashcards

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What is a radical?

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