A radical is a symbol that represents the root of a number, most commonly the square root. For example, $$\text{the square root of } 4 \text{ is represented as } \\sqrt{4} = 2$$ .

How do you simplify $$\text{-3}\\sqrt{8} + 3\\sqrt{18}$$ ?

First, simplify each radical: $$\text{-3}\\sqrt{8} = -3 \times 2\\sqrt{2} = -6\\sqrt{2}$$ and $$3\\sqrt{18} = 3 \times 3\\sqrt{2} = 9\\sqrt{2}$$ . Then combine: $$-6\\sqrt{2} + 9\\sqrt{2} = 3\\sqrt{2}$$ .

What is the product of two radicals, $$\text{specifically } \\sqrt{a} \times \\sqrt{b}$$ ?

The product of two radicals is the square root of the product of the numbers: $$\text{So, } \\sqrt{a} \times \\sqrt{b} = \\sqrt{ab}$$ .

How do you multiply the expression $$(7 - \\sqrt{2})(5 + \\sqrt{3})$$ ?

Use the distributive property (FOIL): $$7 \times 5 + 7 \times \\sqrt{3} - \\sqrt{2} \times 5 - \\sqrt{2} \times \\sqrt{3} = 35 + 7\\sqrt{3} - 5\\sqrt{2} - \\sqrt{6}$$ .

What is the simplified form of $$\text{the expression } \\sqrt{3a^2} \times \\sqrt{15a^2}$$ ?

Combine the radicals: $$\text{This equals } \\sqrt{3 \times 15} \times \\sqrt{a^2 \times a^2} = \\sqrt{45} \times a^2 = 3a^2\\sqrt{5}$$ .

How do you add or subtract radical expressions?

You can only add or subtract radical expressions that have the same radicand (the number under the radical). For example, $$\text{You can combine } 2\\sqrt{3} + 3\\sqrt{3} = 5\\sqrt{3}$$ .

What is the square root of a product?

The square root of a product is equal to the product of the square roots: $$\text{So, } \\sqrt{ab} = \\sqrt{a} \times \\sqrt{b}$$ .

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. For example, $$\text{ } \\sqrt{2} \text{ is irrational}$$ .

What is the value of $$\text{the square root of } 0$$ ?

The square root of 0 is 0, since $$0 \times 0 = 0$$ .

How do you simplify $$\text{the expression } \\sqrt{50}$$ ?

Break it down: $$\text{Since } 50 = 25 \times 2, \\sqrt{50} = \\sqrt{25} \times \\sqrt{2} = 5\\sqrt{2}$$ .

What is the result of $$\text{the expression } 2\\sqrt{3}(\\sqrt{6} - \\sqrt{3})$$ ?

Distribute: $$2\\sqrt{3} \times \\sqrt{6} - 2\\sqrt{3} \times \\sqrt{3} = 2\\sqrt{18} - 6 = 6\\sqrt{2} - 6$$ .

What is the sum of $$\text{the radicals } 4\\sqrt{5} + 2\\sqrt{5}$$ ?

Combine like terms: $$4\\sqrt{5} + 2\\sqrt{5} = 6\\sqrt{5}$$ .

What is the simplified form of $$\text{the expression } \\sqrt{18a^4}$$ ?

Break it down: $$\text{Since } 18 = 9 \times 2, \\sqrt{18a^4} = \\sqrt{9} \times \\sqrt{2} \times a^2 = 3a^2\\sqrt{2}$$ .

Operations with Radicals Flashcards

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1.

FLASHCARD QUESTION

Front

What is a radical?

Back

2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

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4.

FLASHCARD QUESTION

Front

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5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What does it mean to simplify a radical expression?

Back

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

7.

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.

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