Question

STD 8

Find cube root of 4096 by prime factorization​

Answer 1

Answer:16

Step-by-step explanation:

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