HOW TO FIND CUBE ROOT OF A GIVEN NUMBER

Cubes and Cube Root of Class 8

CUBE ROOT THROUGH A PATTERN:

First Pattern:

also 1 + 7 =

also 1 + 7 + 19 =

also

also 1 + 7 + 19 + 37 + 61 =

Second Pattern:

Thus,

and so on.

CUBE ROOT USING UNIT’S DIGIT:

The cube of a number ending in 0, 1, 4, 5, 6 and 9 ends in 0, 1, 4, 5, 6 and 9 respectively.
The cube of a number ending in 2 ends in 8 and vice-versa.
Similarly, the cube of a number ending in 3 or 7 ends in 7 or 3 respectively.

Thus, by looking at the unit’s digit of a perfect cube number, we can find the unit’s digit of the cube-root.

CUBE ROOT BY PRIME FACTORIZATION

To find follow the following steps:

Find the prime factorization of ‘n’.
Group the factors in triples such that all three factors in each triple are the same.
If some prime factors are left ungrouped, the number ‘n’ is not a perfect cube and the process stops.
If no factor is left ungrouped, choose one factor form each group and take their product.
The product is the required cube root of ‘n’.

CUBE ROOT BY HAND:

STEPS:

question 1. Write down the number of which you wish to calculate the cube root, separating the digits into groups of three, starting at the decimal point, from both directions. Draw a cube radical sign over the number, and put a decimal point over the radical directly above the decimal point in the number. For example, let us calculate

question 2. The cube root of 10, so we separate it as 10. 000 000. 2 First digit in cube root done!

question 3. Start with the leftmost group of number(s), and find the biggest integer whose cube is less than or equal to it. Write the integer above the radical, and its cube under the first group. Draw a line under that cube, and subtract it from the first group. In our example, 2^3=8<10<3^3=27, so write 2 over the radical, write 8 under the first group, and subtract it from the first group, resulting in 2.3

Setting up for the next step...

question 4. Bring down the next group of numbers into the remainder, and draw a vertical line to the left of the resulting number. To the left of the vertical line, write three hundred times the square of the number above the radical, a plus sign, thirty times the number above the radical, a multiplication sign, an underscore character, another plus sign, another underscore character, the exponent 2, an equals sign, and some blank space for the answer. For our example, bring down the three 0's. 300 times square of 2 is 1200, 30 times 2 is 60, so write "1200+60*_+_^2=(blank space)" to the left of the vertical line.

Second digit in cube root done!

question 5. Find the biggest integer N that would fit into both underscore places, and give a number in the blank space such that integer N times the number is less than the current remainder. Put the integer N above the radical and into both underscore places, calculate the number to the right of the equal sign, multiply this number by N, write the product under the current remainder, draw a line under that, and subtract to obtain the new remainder. For our example, the integer is 1, 1200+60*1+1²=1261, and 1*1261=1261, which subtracted from 2000 is 739. If the current answer above the radical has the desired accuracy, stop. Otherwise, proceed to the next step.

Setting up for the next step...

question 6. Repeat the previous two steps to find the next digit in the cube root.

Third digit in cube root done!

The result above the radical is the cube root, accurate to three significant figures. In our example, the cube root of 10 is 2.15. Verify that by calculating 2.15^3=9.94, which approximates 10. If you need greater accuracy, simply continue the process.