Find the cube root of the number using prime factorisation method. 46656

To find the cube root of 46656 using the prime factorization method, we need to follow these steps:

### Step 1: Prime Factorization of 46656
We start by dividing 46656 by the smallest prime number (2) and continue dividing until we reach a prime number.

\[
46656 \div 2 = 23328
\]
\[
23328 \div 2 = 11664
\]
\[
11664 \div 2 = 5832
\]
\[
5832 \div 2 = 2916
\]
\[
2916 \div 2 = 1458
\]
\[
1458 \div 2 = 729
\]

Since 729 is not divisible by 2, we now proceed to the next prime number, 3:

\[
729 \div 3 = 243
\]
\[
243 \div 3 = 81
\]
\[
81 \div 3 = 27
\]
\[
27 \div 3 = 9
\]
\[
9 \div 3 = 3
\]
\[
3 \div 3 = 1
\]

So, the prime factorization of 46656 is:

\[
46656 = 2^6 \times 3^6
\]

### Step 2: Group the factors in triplets
Since we are finding the cube root, we group the factors in sets of three:
\[
46656 = (2^6 \times 3^6) = (2^3)^2 \times (3^3)^2
\]

### Step 3: Take the cube root
Now, we take the cube root by taking one factor from each group:
\[
\sqrt[3]{46656} = 2^2 \times 3^2 = 4 \times 9 = 36
\]

### Final Answer:
The cube root of 46656 is \( 36 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How can we use prime factorization to find the square root of a number?
2. Why do we group factors into triplets when finding the cube root?
3. What is the prime factorization of 729?
4. Can you find the cube root of a number like 5832 using the same method?
5. How is the prime factorization method different from using a calculator for cube roots?

**Tip:** Prime factorization is helpful for finding cube roots, square roots, and simplifying fractions!

Learn how to find the cube root of 46656 using the prime factorization method with a detailed step-by-step breakdown. This guide covers key concepts such as prime factorization and exponentiation, suitable for students in Grades 6-8.

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