Question

show that 729 is a perfect cube

Answer 1

Given: The number 729

To find: Show that its a perfect square.

Solution:

• Now the number given is 729. By prime factorisation, we get:

                     3 | 729

                     3 | 243

                     3 | 81

                     3 | 27

                     3 | 9

                     3 | 3

                        | 1

• So the factors are:

               729 = 3 x 3 x 3 x 3 x 3 x 3

• Taking square root on both sides, we get:

              √729 = √(3 x 3 x 3 x 3 x 3 x 3)

              √729 = 3 x 3 x 3

              √729 = 27

Answer:

           So the square root is 27.