Question

find the cube root of 10000 by prime factorization method ​

Answer 1

Step-by-step explanation:

10,000 can be written as a product of its prime factors in the following way: 10,000 = 24 × 54

The factors were found in the following order:

10,000 = 2 × 5,000

5,000 = 2 × 2,500

2,500 = 2 × 1,250

1,250 = 2 × 625

625 = 5 × 125

125 = 5 × 25

25 = 5 × 5

Step 2: Rewrite ∛(10,000)

∛(10,000) =

∛(24 x 54) =

∛(24) × ∛(54)

∛(24 x 54) = ∛(24) x ∛(54)

Step 3: Simplify ∛(24) x ∛(54)

Step 3.1 Rewrite ∛(24)

∛(24) = ∛(23) × ∛(21)

Step 3.2 Rewrite ∛(54)

∛(54) = ∛(23) × ∛(21) × ∛(53) × ∛(51)

Step 4: Simplify ∛(24) x ∛(54)

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 ∛(21)

As per raising to the power of one: 2^1 = 2

So, we can rewrite ∛(21) = ∛(2) = 1.25992104989487

Step 4.3 Simplify ∛(53)

Using the exponent "product rule", we know that

∛(53) = ((5)3)⅓ = 5(3×⅓) = 51 = 5

Step 4.4 Simplify ∛(51)

As per raising to the power of one: 5^1 = 5

So, we can rewrite ∛(51) = ∛(5) = 1.7099759466767

Final Result

∛(10,000) = 2 × 1.25992104989487 × 5 × 1.7099759466767

One real solution was found

21.5443469003188

Answer 2

find the cube of 10,000?