Answers FL-1200370-Algebra 1-A Semester 2 The Square Root FunctionQuestion 77105

77105

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The Square Root Function

Question 77105 • FL-1200370-Algebra 1-A Semester 2

The prime factorization of 576 is [___].

Answer

A

2(2)(2)(2)(2)(2)

B

2(2)(2)(2)(3)(3)

C

2(2)(2)(2)(2)(2)(3)(3)

D

2(2)(2)(2)(3)(3)(3)(3)

Explanation

Divide 576 by 2 repeatedly: 576 = 2 × 288 = 2² × 144 = 2³ × 72 = 2⁴ × 36 = 2⁵ × 18 = 2⁶ × 9. Since 9 = 3², the prime factorization is 2⁶ × 3², or six factors of 2 and two factors of 3. That matches choice C.

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