A number greater than 1000, whose prime factorization includes one non-repeating prime number, one prime number repeated three times, and another prime number repeated twice. I also don't know how to find the square root, so please don't suggest that.

To find a number greater than 1000 with the given prime factorization conditions, we have to select appropriate prime numbers—one that does not repeat, one that repeats three times, and another that repeats twice. Let's pick some small prime numbers to make the computation simple.

Non-repeating prime number: Let's choose 2 Prime number repeated three times: Let's choose 3 (which would give us \( 3^3 = 27 \)) Prime number repeated twice: Let's choose 5 (which would give us \( 5^2 = 25 \))

Now we multiply these together to get the number: Number = 2 × 27 × 25 Number = 2 × (3 × 3 × 3) × (5 × 5) Number = 2 × 3^3 × 5^2 Number = 2 × 27 × 25 Number = 54 × 25 Number = 1350

So, 1350 is a number that satisfies the conditions.

Extra: Prime factorization is the process of breaking down a composite number into its prime factors, which when multiplied together give the original number. Prime numbers are numbers that have exactly two distinct positive divisors: 1 and the number itself.

For example, the prime factors of 18 are 2 and 3, since 18 can be written as \( 2 × 3 × 3 \) (or \( 2 × 3^2 \)).

When finding a number as per specific prime factorization criteria, like in your query, you typically have to choose prime numbers that fit the criteria and then multiply them together to get the composite number. You don't need to find the square root in this process, which is good since you mentioned you're not familiar with that operation.

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 multiplied by 5 is 25. Square roots are relevant for prime factorization when dealing with squared prime numbers (like \( 5^2 \) in our example), but only the prime factors themselves are necessary to satisfy the conditions you've provided.