A two-digit number, A perfect square, A power of 3, The digit product < 10

Find the number that satisfies all of the following conditions: A

For a square to be a power of three, the original number itself must be a power of 3, namely 3, 9, 27, etc.

Which of the squares of these numbers satisfies all of the above conditions?

Is the answer 81?

Correct! Well done!

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To find a number that satisfies all of these conditions, we need to go through each condition step by step.

First, we need a two-digit number. A two-digit number is any number between 10 and 99 (inclusive).

Next, we need to find a perfect square. A perfect square is a number whose square root is a whole number. We can start by checking the square of each two-digit number.

For example, we can check if 10 squared (10^2 = 100) is a perfect square. However, 100 is not a perfect square because its square root is 10, which is not a whole number.

We can continue checking the squares of the two-digit numbers until we find one where the square root is a whole number. And if we don't find one, it means there is no two-digit number that satisfies this condition.

Now, we move on to finding a power of 3. A power of 3 is any number that can be expressed as 3 raised to some exponent. We can start by checking if any of the two-digit numbers can be expressed as a power of 3.

For example, we can check if 11 can be expressed as a power of 3. However, 11 is not a power of 3.

We can continue checking the remaining two-digit numbers until we find one that can be expressed as a power of 3. If we don't find one, it means there is no two-digit number that satisfies this condition.

Finally, we need to find a number where the product of its digits is less than 10. For example, for the number 27, the product of its digits (2 * 7) is 14, which is not less than 10.

We need to check each two-digit number and calculate the product of its digits. If the product is less than 10, we have found a number that satisfies this condition.

Continuing the process, we can find that the number 81 satisfies all the conditions. It is a two-digit number, a perfect square (9^2 = 81), a power of 3 (3^4 = 81), and the product of its digits (8 * 1) is less than 10.

So, the number that satisfies all the given conditions is 81.