Question

Find the cube root of the following numbers step by step. 1)5832 2)4096 Send me right answer I will make you brainliest if you send me wrong answer I will report your answer because this question is of 100 points

Answer 1

Answer:

1》》》》

5832

=3×3×3×3×3×3×2×2×2

=3×3×2

=18

2》》》》

Step 1: Factor 4,096

4,096 can be written as a product of its prime factors in the following way: 4,096 = 212

The factors were found in the following order: 

4,096 = 2 × 2,048

2,048 = 2 × 1,024

1,024 = 2 × 512

512 = 2 × 256

256 = 2 × 128

128 = 2 × 64

64 = 2 × 32

32 = 2 × 16

16 = 2 × 8

8 = 2 × 4

4 = 2 × 2

2 = 2 × 1

Step 2: Rewrite ∛(4,096)

∛(4,096) =

∛(212) =

∛(212)

∛(212) = ∛(212)

Step 3: Simplify ∛(212)

Step 3.1 Rewrite ∛(212)

∛(212) = ∛(23) × ∛(23) × ∛(23) × ∛(23)

Step 4: Simplify ∛(212)

Step 4.1 Simplify ∛(23)

Using the exponent "product rule", we know that 

∛(23) = ((2)3)⅓ = 2(3×⅓) = 21 = 2

Step 4.2 Simplify ∛(23)

Using the exponent "product rule", we know that 

∛(23) = ((2)3)⅓ = 2(3×⅓) = 21 = 2

Step 4.3 Simplify ∛(23)

Using the exponent "product rule", we know that 

∛(23) = ((2)3)⅓ = 2(3×⅓) = 21 = 2

Step 4.4 Simplify ∛(23)

Using the exponent "product rule", we know that 

∛(23) = ((2)3)⅓ = 2(3×⅓) = 21 = 2

Final Result

∛(4,096) = 2 × 2 × 2 × 2

One real solution was found

16

Answer 2

Answer:

4096 is said to be a perfect cube because 16 x 16 x 16 is equal to 4096. Since 4096 is a whole number, it is a perfect cube. The nearest previous perfect cube is 3375 and the nearest next perfect cube is 4913 . 4096 is said to be a perfect cube because 16 x 16 x 16 is equal to 4096.

The principal, real, root of:

5832−−−−√3

=18

All roots:

18

−9+15.5884573i

−9−15.5884573i

5832 is a perfect cube

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