Question

A gardener has 1012 plants.He wants to plant these in such a way that the number of rows and the number of columns remain same.Find the minimum number of plants he needs more for this.

Answer 1

Minimum number of plants he needs to plant in such a way that rows and columns remain same

1012 + x = 32*32 = 1024

x = 1024 - 1012 = 12 Ans.

Step-by-step-explanation

Gardener has 1012 plants at present

to plant these in such a way that the number of rows and the number of columns remain same

To make 3*3 = 9 plants required

30*30 = 900 plants required < 1012

31*31 = 961 plants required < 1012

32*32 = 1024 plants required > 1012

so, if he get 1024 - 1012 = 12 more plants, he can plant them in such a way that rows and columns remain same i.e. 32*32

         plant           plant           plant       ...............32 times

         plant           plant           plant       ...............32 times

         plant           plant           plant       ...............32 times

         .                   .                  .               ...............32 times

         .                   .                  .               ...............32 times

         .                   .                  .               ...............32 times

        32 times      32 times    32 times   ...............32 times

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Answer 2

Given:  A gardener has 1012 plants.He wants to plant these in such a way that the number of rows and the number of columns remain same

To find : the minimum number of plants he needs more for this

Solution:

Let say number of rows  & column = n

then plants required = n²

n²  ≥ 1012

=> n  ≥  √1012

√1012 = 31.8

=> n = 32

n² = 32²  = 1024

number of plants needed = 1024

number of plant gardener has = 1012

the minimum number of plants gardener needs more  = 1024 - 1012 = 12

Minimum 12 more plants are required by gardener

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