Find the cube root of 132651 by prime factorization method.
Answers
Answer:
51
Step-by-step explanation:
SWe attempt To simplify the cubed root Of 132,651
Step 1: Factor 132,651
132,651 can be written as a product of its prime factors in the following way: 132,651 = 33 × 173
The factors were found in the following order:
132,651 = 3 × 44,217
44,217 = 3 × 14,739
14,739 = 3 × 4,913
4,913 = 17 × 289
289 = 17 × 17
Step 2: Rewrite ∛(132,651)
∛(132,651) =
∛(33 x 173) =
∛(33) × ∛(173)
∛(33 x 173) = ∛(33) x ∛(173)
Step 3: Simplify ∛(33) x ∛(173)
Step 3.1 ∛(33) shall be further simplified in the next step
Step 3.2 ∛(173) shall be further simplified in the next step
Step 4: Simplify ∛(33) x ∛(173)
Step 4.1 Simplify ∛(33)
Using the exponent "product rule", we know that
∛(33) = ((3)3)⅓ = 3(3×⅓) = 31 = 3
Step 4.2 Simplify ∛(173)
Using the exponent "product rule", we know that
∛(173) = ((17)3)⅓ = 17(3×⅓) = 171 = 17
Final Result
∛(132,651) = 3 × 17
One real solution was found
51
Answer:
51
Step-by-step explanation:
132651 = 3 × 3 × 3 × 17 × 17 × 17
= 3³ × 17³
Cancel the cube root and cube
Ans: 51