Is 90209 a perfect square? Use the long division method to find out. If yes, find its square root using long division. If no, write the remainder that you obtain using long division.

Answer:

To determine if 90209 is a perfect square, let's use the long division method:

First, find the closest perfect square below 90209, which is 300^2 = 90000.

Subtract 90000 from 90209, which gives us a remainder of 209.

Since we have a remainder after division, 90209 is not a perfect square.

The remainder obtained through long division is 209.

Final Answer:

90209 is a perfect square, and its square root using the long division method is 301.

Explanation:

To determine if 90209 is a perfect square, we can use the long division method to find its square root.

Step 1: Start by grouping the digits in pairs from right to left: 90, 20, and 9.

Step 2: Find the largest number whose square is less than or equal to 90. In this case, it's 9, as = 81. Write 9 as the first digit of the square root.

Step 3: Subtract 81 from 90, leaving 9 as the remainder.

Step 4: Bring down the next pair of digits, which is 20, and append them to the remainder, making it 920.

Step 5: Find the largest number whose square is less than or equal to 920. It's 30, as = 900. Write 30 as the next digit of the square root.

Step 6: Subtract 900 from 920, leaving 20 as the remainder.

Step 7: Bring down the last pair of digits, which is 09, and append them to the remainder, making it 2009.

Step 8: Find the largest number whose square is less than or equal to 2009. It's 1, as = 1. Write 1 as the final digit of the square root.

Now, we have the square root of 90209 as 301, and since we were able to divide it into perfect square factors without any remainder, we can conclude that 90209 is indeed a perfect square.

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