Math, asked by lakshyasaraswat5678, 8 months ago

Find the cube root of 132651 by prime factorization method.​

Answers

Answered by yashnandnimahi56
1

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

Answered by sanjayk804078
3

Answer:

51

Step-by-step explanation:

132651 = 3 × 3 × 3 × 17 × 17 × 17

= 3³ × 17³

 \sqrt{132651}  =  \sqrt{(3 \times 17) {}^{3} }  \\  = 3 \times 17 \\  = 51

Cancel the cube root and cube

Ans: 51

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