Question

finding the cube root of 3375

Answer 1

3375= 3*3*3*5*5*5
therefore
3375⅓=(3*3*3*5*5*5)⅓
3375⅓=3*5=15

Answer 2

Step-by-step explanation:

$\begin{array}{c | c }3 & 3375 \\ \cline{2-2} 3 & 1125 \\ \cline{2-2} 3 & 375 \\ \cline{2-2} 5 & 125 \\ \cline{2-2} 5 & 25 \\ \cline{2-2} & 5\end{array}$

Therefore,

3375 = (3x3x3) x (5x5x5) = 3³ x 5³

Therefore,

$\sqrt[3]{3375}$ = 3 x 5 = 15

Cube roots:

Cube root of a positive perfect cube

By prime factorization

Steps:

1. Express the number as a product of its prime factors.
2. Make triplets of equal prime factors.
3. Take one factor from each triplet and multiply them.

You can also Express the number as a product of power of the prime factors.

Then, dividing each index of those power by 3 and multiplying the factors will give you the cube root.