Vedic Math

Cubes and Cube Roots

Published: 03rd September 2015 10:24 AM  |   Last Updated: 03rd September 2015 10:24 AM   |  A+A-

Last week we discussed cubes, this week let us go one step further and discuss cube roots. Just like in squares, it is first important to know the cubes table for numbers 1 to 10. If we know this we can calculate the cube root of the perfect cube number mentally just by looking at the number. So let us first get familiar with the cube of the first ten numbers from the table below:

 

Kumudha Krishnan.jpgWe can deduce the following points from this:

  • The units digit of any cube is unique.
  • The cube of 1 is 1 and  that of 11 is 1331. So any number with 1 as the

units digit will have 1 as the units digit in its cube.

  • Numbers with 4, 5, 6, 9 and 0 in the units place will have the same

number in the units place in the cube.

  • The cube of 2 has 8 and the cube of 8 has 2 in the units place.
  • The cube of 3 has 7 and the cube of 7 has 3 in the units place.
  • The cube of any number ending with zero has a minimum of 3 zeros in its final digits.

One special fact about a cube is that the digit sum of a perfect cube will be 1, 8 or 9. This fact can be used to check whether a number is a perfect cube or not.

 

 

Let us check whether the following numbers are perfect cubes or not.

Consider 79507

 

  • First let us find the sum of the digits. 7 + 9 + 5 + 0 + 7 = 28 = 2 +8 = 1. So it may be a perfect cube.
  • It ends with 7, so the cube root will end with 3.

 

Consider 17562

  • The sum of the digits is 1 + 7 + 5 + 6 + 2 = 21 = 3. So we know  it is not a perfect cube.

 

What will be in the unit’s digit of the cube of 36?

  • Answer: 6, because we know that a number that ends with 6 will have a cube that ends with 6.

 

What can you say about the units digit of the cube of 87?

  • Its units digit is 7 so the cube will have 3 as the units digit.

 

Now check which of these may be a perfect cube?

456533

42876

238328

157466

 

Tip of the week: Understanding concepts will helps us to solve any problem. 

Stay up to date on all the latest Bengaluru news with The New Indian Express App. Download now
(Get the news that matters from New Indian Express on WhatsApp. Click this link and hit 'Click to Subscribe'. Follow the instructions after that.)

Comments

Disclaimer : We respect your thoughts and views! But we need to be judicious while moderating your comments. All the comments will be moderated by the newindianexpress.com editorial. Abstain from posting comments that are obscene, defamatory or inflammatory, and do not indulge in personal attacks. Try to avoid outside hyperlinks inside the comment. Help us delete comments that do not follow these guidelines.

The views expressed in comments published on newindianexpress.com are those of the comment writers alone. They do not represent the views or opinions of newindianexpress.com or its staff, nor do they represent the views or opinions of The New Indian Express Group, or any entity of, or affiliated with, The New Indian Express Group. newindianexpress.com reserves the right to take any or all comments down at any time.

flipboard facebook twitter whatsapp