Question

A gardener has 1750 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

Answer:

Minimum number of plants he needs more is 14.

Step-by-step explanation:

The gardener wants to equalize the number of rows and number of columns.

That means number of plants in each row = number of plants in each column.

If there are 'N' plants in one row then 'N' number plants will be there in one column. So total number of plants = N × N = N².

The number of plants must be an integer which is perfect square.

1750 is not a perfect square. The nearby perfect square is 1764.

1764 = 42². The gardener needs to plant 42 plants in each row and in each column.

To make that he needs  1764 - 1750 = 14 more plants.

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Answer 2

Answer:

The minimum number of plants he need more is 14.

Step-by-step explanation:

Given:-

A gardener has 1750 plants.

He wants to plant in such a way that the number of rows and the number of columns remains the same.

To find:-

The minimum no. of plants he need more.

Step 1 of 1

According to the question,

The total number of plants = 1750

Since the number of rows is $equal$ to the number of columns.

We need to make the number 1750 a perfect square by adding a minimum number.

Observe that,

The square of the number 41 is 1681, i.e.,

$41^2 < 1750$

So, the square of number 42 is 1764.

Hence,

1764 - 1750 = 14

Thus, 14 more plants are required to make the number of rows equal to the number of columns.

Final answer: The minimum number of plants he need more is 14.

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