A gardener had 335250 flower saplings with him to show in his field which was in the form of a square. He found that 9 saplings more in number. How many flowers are there in each r... A gardener had 335250 flower saplings with him to show in his field which was in the form of a square. He found that 9 saplings more in number. How many flowers are there in each row?
Understand the Problem
The question is asking for the number of flower saplings arranged in each row of a square-shaped field, given that the total number of saplings is 335250 and that there are 9 more saplings than a perfect square number. We will determine the side length of the square and how many flowers are in each row.
Answer
The number of flower saplings arranged in each row is \( 579 \).
Answer for screen readers
The number of flower saplings arranged in each row is ( 579 ).
Steps to Solve
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Identify the perfect square number Since the total number of saplings is 335250, and it is 9 more than a perfect square number, we can express this as: $$ 335250 = n^2 + 9 $$ where $n^2$ is the perfect square. Rearranging gives: $$ n^2 = 335250 - 9 = 335241 $$
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Calculate the square root To find $n$, we will take the square root of 335241: $$ n = \sqrt{335241} $$ Calculating this gives approximately: $$ n \approx 579 $$
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Find the number of saplings in each row Since the flowers are arranged in a square shape, the number of saplings per row is equal to the side length of the square. Therefore, the side length is: $$ s = n = 579 $$
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Verification of the perfect square To ensure this solution is correct, we can check if: $$ 579^2 + 9 = 335250 $$ Calculating $579^2$: $$ 579^2 = 335241 $$ And adding 9 confirms: $$ 335241 + 9 = 335250 $$
The number of flower saplings arranged in each row is ( 579 ).
More Information
The perfect square number closest to the total saplings (335250) is 335241, which is the square of 579. This means the arrangement is nearly complete but just has 9 extra saplings.
Tips
- Not correctly calculating the square root of the perfect square. Always double-check that the square root calculation is accurate, as rounding errors can mislead the final side length.
- Misunderstanding the arrangement of saplings; they must be arranged in a complete square, so the side must be the whole number square root.
