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 $$\text{the square root of } 50$$ ?

$$\text{The square root of } 50 \text{ simplifies to } 5\text{√}2$$ .

What is $$\text{the square root of } 256$$ ?

$$\text{The square root of } 256 \text{ is } 16$$ .

What is $$\text{the square root of } 216$$ ?

$$\text{The square root of } 216 \text{ simplifies to } 6\text{√}6$$ .

What is $$\text{the square root of } 45$$ ?

$$\text{The square root of } 45 \text{ simplifies to } 3\text{√}5$$ .

What is $$\text{the square root of } 300$$ ?

$$\text{The square root of } 300 \text{ simplifies to } 10\text{√}3$$ .

What does it mean to 'simplify a radical'?

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

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.

What is the simplified form of $$\text{the square root of } 72$$ ?

$$\text{The square root of } 72 \text{ simplifies to } 6\text{√}2$$ .

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

$$\text{The square root of } 18 \text{ simplifies to } 3\text{√}2$$ .

What is the relationship between radicals and exponents?

Radicals can be expressed as exponents. For example, $$\text{the square root of } x \text{ is the same as } x^{1/2}$$ .

What is the product property of radicals?

The product property states that $$\text{the square root of a product is equal to the product of the square roots: } \\sqrt{a \times b} = \\sqrt{a} \times \\sqrt{b}$$ .

What is the quotient property of radicals?

The quotient property states that $$\text{the square root of a quotient is equal to the quotient of the square roots: } \\sqrt{\frac{a}{b}} = \frac{\\sqrt{a}}{\\sqrt{b}}$$ .

Simplify Radicals Flashcards

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1.

FLASHCARD QUESTION

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What is a radical?

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2.

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To simplify radicals, factor the number under the radical into its prime factors, then pair the factors. Each pair can be taken out of the radical as a single number.

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