Q. Find the squares of the following numbers containing 5 in unit’s place.

(iv) 205

Answers (1)

Consider a number with unit digit 5, i.e.,    a5

(a5)^{2} = (10a + 5)^{2} = 10a(10a + 5) + 5(10a + 5) = 100a 2 + 50a + 50a + 25

                            = 100a(a + 1) + 25

                            = a(a + 1) hundred + 25.

Here a = 20

Hence 205^{2}    =    20(20+1)hundred + 25

                         =   20(21)hundred + 25 = 42000 + 25

                        =   42025

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