What does it mean to simplify a radical expression?

It means to rewrite the expression in a simpler form, often by removing perfect squares or cubes from under the radical.

How do you determine if a number is a perfect square?

A number is a perfect square if it can be expressed as the square of an integer.

What is the relationship between radicals and exponents?

Radicals can be expressed as exponents: $$\sqrt{a} = a^{1/2}$$ .

Simplifying Radicals Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

2.

FLASHCARD QUESTION

Front

How do you simplify a radical?

Back

To simplify a radical, factor the number under the root into its prime factors and look for pairs of factors to take out of the radical.

3.

FLASHCARD QUESTION

Front

What is the square root of 196?

Back

14, because $14^2 = 196$ .

4.

FLASHCARD QUESTION

Front

Simplify: $-3\sqrt{84}$

Back

$-6\sqrt{21}$ .

5.

FLASHCARD QUESTION

Front

What is the prime factorization of $20$ ?

Back

$5 \cdot 2 \cdot 2$ .

6.

FLASHCARD QUESTION

Front

Factor $\sqrt{x^3}$

Back

$\sqrt{x \cdot x \cdot x}$ .

7.

FLASHCARD QUESTION

Front

What is the simplified form of $3x \sqrt{50x^2y}$ ?

Back

$15x^2 \sqrt{2y}$ .

9.

FLASHCARD QUESTION

Front

What is the square root of a product?

Back

$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ .

10.

FLASHCARD QUESTION

Front

What is the square root of 200?

Back

$10\sqrt{2}$ .

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