Question

4. A gardener has 1000 plants. He wants to plant
these in such a way that the number of rows and
the number of columns remain the same. Find the
minimum number of plants he needs more for this
​

Answer 1

Step-by-step explanation:

the number of rows and number of columns are to be equal, then the total number of trees will be in the form of x2, which is nothing but a perfect square.

As 1000 is not a perfect square, you need to check for a perfect square above and nearest to 1000.

It's 1024, which is square of 32. So he needs to add 24 more trees to get 1024.

Answer 2

Answer:

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Step-by-step explanation:

Given : Total Plants = 1000

And number of rows is equal to the number of columns

Let Number of rows = x

∴ Number of columns = x

Now,

Total Plants = Number of Rows x Number of columns

1000 = x * x

1000 = x^2

x^2 = 1000

x = $\sqrt{1000\\}$

Finding Square root of 1000 using Long Division (in image 1)

Here,  Remainder = 39

Given that,

He wants to plant these in such a way that the number of rows and

the number of columns remain same, we need to find the minimum

number of plants he needs more for this.

We need to find  the least number that must be added to 1000 so as to get a perfect  square.

Now,

31^2 < 1000 < 32^2

Thus, we add 32^2 – 1000 to the number

∴ Number to added = 32^2 - 1000

= 1024 - 1000

= 24

The Gardner needs 24 more plants.