CLASS-7
FINDING CUBE ROOT OF DECIMAL NUMBERS

FINDING CUBE ROOT OF DECIMAL NUMBERS -

Finding the cube root of a decimal number with a fraction part can be done using different approaches. Here are some effective methods:

Express the given decimal in the fraction form and then find the cube root of the numerator and denominator separately and convert the same into decimal.

Example:-

What is the cube root of 0.343?

Ans.)

0.343 has a whole number part, which is 0, and the fractional part, which is 343.

Step.1:- The first step is to express the number as a fraction with a numerator and a denominator.

          0.343 = 343 / 1000

The numerator is 343, and the denominator is 1000


Step.2:- The next step is to find the cube root of both the numerator and the denominator using the method of factorisation explained in the examples above.

Let's look at the prime factors of 343, which is not divisible by 2, 3, or 5. It is divisible by 7.

·  343 / 7 = 49

·   49 / 7 = 7

·    7 / 7 = 1

·  343 = 7 * 7 * 7

For the denominator, we already know that 1000 = 10 * 10 * 10


Step.3:-

Pick the factors that occur three times: 7 for the numerator and 10 for the denominator.

Hence the cube root of 343 / 1000 = 7 / 10.

The cube root of 0.343 is the same as the cube root of 343/1000 = 7/10 = 0.7.

So the cube root of 0.343 = 0.7.


Example.2) Find cube root of ∛729

Ans.)

Roots

Types Of Finding Cube Root:-

1. Converting to Fraction Form:-

If the decimal can be easily written as a fraction, take the cube root of both numerator and denominator.

Example.3)  ∛0.125

Ans.)

                                             125

  • Rewrite as a fraction:-   0.125 = --------                   

                                             1000

  • Take the cube root of both the numerator and denominator:-

                        ∛125 =  ∛5³ = 5     and    ∛1000 = ∛10³ = 10

                        5

  • So, ∛0.125 = ------- =  0.5

                       10


2) Estimation Method:-

If the decimal isn’t easily converted to a fraction, find nearby perfect cubes.

Example.4)   ∛2.5 

  • Find perfect cubes around 2.5

         2.5 is between 1 & 8 which is 1³ & 2³

     So, 1 = ∛1³ = 1  and,

          8 = ∛2³ = 2

  • Since 2.5 is between 1 and 8, the cube root is between 1 and 2.
  • A better approximation is 1.35.


3) Using Logarithms:-

If you want an accurate manual method:

  • Take the logarithm:

                    x = ∛N

                           1

            ⇒ log x = ------- ​log N

                           3

  • Use logarithm tables or a calculator, then take the antilog.


4) Long Division Method for Cube Roots:-

This is a manual method similar to finding square roots by division but requires a bit more calculation.