Question

explain the method of finding cube root by prime factorization method and harrdy Ramanujan number with two examples ​

Answer 1

Answer:

Hey mate! Here's your answer:

Step-by-step explanation:

We have to do the usual prime factorisation first.

All the prime numbers have to come in groups of 3, which are more specifically called triplets.

Take 1 number from each triplet and multiply them.

The final product is your required Cube Root!

Example: Find the cube root of 216 by prime factorisation.

216 = 3 * 3 * 3 * 2 * 2 * 2.

3 and 2 are coming in triplets.

So Cube Root of 216 = 3 * 2 = 6.

Hardy - Ramanujan numbers are those numbers which can be expressed as the sum of two cubes in two different ways.

Examples: 1729 = 1³ + 12³ or 9³ + 10³.

4104 = 2³ + 16³ or 9³ + 15³.

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