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

What is the simplified form of $$\text{the radical } \\sqrt{121v}$$ ?

The simplified form is $$11\text{ }\\sqrt{v}$$ .

What is the simplified form of $$\text{the radical } \\sqrt{75x^2}$$ ?

The simplified form is $$5x\text{ }\\sqrt{3}$$ .

What is the simplified form of $$\text{the radical } \\sqrt{144k^3}$$ ?

The simplified form is $$12k\text{ }\\sqrt{k}$$ .

What is the simplified form of $$\text{the radical } \\sqrt{252xy^2z^3}$$ ?

The simplified form is $$6yz\text{ }\\sqrt{7xz}$$ .

What is the simplified form of $$\text{the radical } \\sqrt{196c^5d^2}$$ ?

The simplified form is $$14c^2d\text{ }\\sqrt{c}$$ .

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.

What is the product property of square roots?

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

What is the quotient property of square roots?

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

How do you handle variables under a radical?

For variables under a radical, if the exponent is even, you can take the square root. For example, $$\text{for } x^2, \\sqrt{x^2} = x$$ .

What is the simplified form of $$\text{the radical } \\sqrt{16x^4}$$ ?

The simplified form is $$4x^2$$ .

What is the simplified form of $$\text{the radical } \\sqrt{50y^3}$$ ?

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

What is the simplified form of $$\text{the radical } \\sqrt{81m^6n^2}$$ ?

The simplified form is $$9m^3n$$ .

Simplifying Radicals with Variables Flashcards

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FLASHCARD QUESTION

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What is a radical?

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2.

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To simplify radicals with variables, factor the expression under the radical into perfect squares and other factors. Then, take the square root of the perfect squares out of the radical.

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