Short Tricks to Find Cube Root

Any integer can have its cube root difficult to find, however there are various methods and shortcuts to make the job easier. Here are a few methods:

Digit by Digit Method

• Step 1: Find the digital root of the number by repeatedly summing the digits until you get a single digit. For example, the digital root of 1728 (1 + 7 + 2 + 8 = 18, 1 + 8 = 9).
• Step 2: Use the digital root to narrow down the possibilities, as the cube root of a number often has a specific digital root pattern. While this method is not always precise, but it can help in estimating.

Using Prime Factorization

• Step 1: Factor the number into its prime factors. For example, for 216, the factorization is 2³×3³.
• Step 2: Group the factors into triples. Here, 2³ and 3³are already grouped.
• Step 3: Take one factor from each group. The cube root of 2³×3³ is 2×3=6.

Estimation Method

• Step 1: Find two perfect cubes between which the number lies. For example, if you want to find the cube root of 50, you know it lies between 3³=27 and 4³=64.
• Step 2: Estimate the value between these two numbers. Since 50 is closer to 64 than to 27, you can guess the cube root to be closer to 4.
• Step 3: To obtain a closer estimate, average your prediction or use trial and error.

Finding the cube root of a large number is difficult. Simple shortcuts make the procedure faster and easier. These shortcuts use basic patterns and straightforward steps to find the cube root without complex calculations or advanced tools.

This method is useful for saving time and improving mental math skills. By learning these techniques, one can easily determine the cube root of any number.