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

What is the simplest form of $$\text{-}\\sqrt{320}$$ ?

The simplest form is $$-8\\sqrt{5}$$ .

How do you simplify $$\text{-5}\\sqrt{12} \times \\sqrt{8}$$ ?

The simplified form is $$-20\\sqrt{6}$$ .

What is the simplified form of $$\text{the expression } \\sqrt{147} - \\sqrt{48}$$ ?

The simplified form is $$3\\sqrt{3}$$ .

What is the square root of 64?

The square root of 64 is 8, since $$8 \times 8 = 64$$ .

What is the principle of combining like radicals?

Like radicals can be combined by adding or subtracting their coefficients. For example, $$3\\sqrt{2} + 5\\sqrt{2} = 8\\sqrt{2}$$ .

What is the simplified form of $$6\text{ }\\sqrt{2} - 6\text{ }\\sqrt{5}$$ ?

The expression is already in its simplest form.

What is the process of multiplying radicals?

To multiply radicals, multiply the numbers under the radical signs and then simplify if possible. For example, $$\text{ } \\sqrt{a} \times \\sqrt{b} = \\sqrt{ab}$$ .

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

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

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.

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

The simplified form is $$6\\sqrt{2}$$ .

What is the significance of simplifying radicals in mathematics?

Simplifying radicals makes calculations easier and helps in solving equations more efficiently.

Simplifying Radicals (Without Variables) Flashcards

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1.

FLASHCARD QUESTION

Front

What is a radical?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to simplify a radical?

Back

To simplify a radical means to express it in its simplest form, removing any perfect square factors from under the radical sign.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is a perfect square?

Back

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.

7.

FLASHCARD QUESTION

Front

How do you identify perfect square factors in a radical?

Back

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