The square root of a number x is a value y such that $$y^2 = x$$ . It is denoted as $$\text{sqrt}(x)$$ .

The cube root of a number x is a value y such that $$y^3 = x$$ . It is denoted as $$\text{cbrt}(x)$$ .

What is the prime factorization of 120?

$$120 = 2^3 \times 3 \times 5$$ .

Explain how to simplify square roots with prime factorization.

To simplify a square root, factor the number into its prime factors, pair them, and take one from each pair out of the square root.

Explain how to simplify cube roots with prime factorization.

To simplify a cube root, factor the number into its prime factors, group them in threes, and take one from each group out of the cube root.

What is the relationship between square roots and exponents?

The square root of a number can be expressed as an exponent: $$\text{sqrt}(x) = x^{1/2}$$ .

Simplifying Square and Cube Roots Flashcards

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FLASHCARD QUESTION

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Define square root.

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