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SAI International School
                                                         Class VIII

               Mathematics
               Chapter 7 – CUBES AND CUBE ROOTS
               Lesson notes
               Subtopic: Prime factorisation and estimation



               Cube roots:

                   Finding the square root, as you know, is the inverse operation of squaring. Similarly,
               finding the cube root is the inverse operation of finding cube.
                                3
               We know that 2  = 8; so we say that the cube root of 8 is 2.
               We write       = 2. The symbol   denotes ‘cube-root.’





















                       Cube root through prime factorisation:

               Consider 3375. We find its cube root by prime factorisation:
                                                 3
                                                      3
                                                                 3
               3375 = 3 × 3 × 3 × 5 × 5 × 5 = 3  × 5  = (3 × 5)
               Therefore, cube root of 3375 =  3375 = 3 × 5 = 15
               Example 1: Find the cube root of 8000.
               Solution: Prime factorisation of 8000 is 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5
               So,  8000 = 2 × 2 × 5 = 20


               Example 2: Find the cube root of 13824 by prime factorisation method.
                                                                               3   3    3   3
               Solution:13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2 × 2 × 2 × 3 .
               Therefore,  13824 = 2 × 2 × 2 × 3 = 24




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