Understanding the Question: Square Root of 2025

The question asks us to find the number which, when multiplied by itself, equals 2025. This is known as finding the square root of 2025. We are given four options and need to determine the correct one.

Calculating the Square Root of 2025

There are a few ways to find the square root of 2025. We can use prime factorization or check the squares of the given options.

Method 1: Prime Factorization

Let's break down 2025 into its prime factors:

• Since 2025 ends in 5, it is divisible by 5. $2025 \div 5 = 405$
• 405 also ends in 5, so it's divisible by 5. $405 \div 5 = 81$
• 81 is divisible by 9 (and 3). Let's use 9. $81 \div 9 = 9$
• 9 is $3 \times 3$, or $9 \times 1$. We already have 9. $9 \div 9 = 1$

So, the prime factorization of 2025 is $5 \times 5 \times 9 \times 9$. We can write this as:

$2025 = 5^2 \times 9^2$

To find the square root, we take one factor from each pair:

$\sqrt{2025} = \sqrt{5^2 \times 9^2} = \sqrt{5^2} \times \sqrt{9^2} = 5 \times 9 = 45$

Method 2: Checking the Options

We can also check the square of each option provided:

• Option 1: $35^2 = 35 \times 35 = 1225$. This is not 2025.
• Option 2: $45^2 = 45 \times 45$. Let's calculate this:

  $45 \times 45 = (40 + 5) \times (40 + 5)$ $= 40 \times 40 + 40 \times 5 + 5 \times 40 + 5 \times 5$ $= 1600 + 200 + 200 + 25$ $= 1600 + 400 + 25$ $= 2025$

  This matches the number given in the question.
• Option 3: $55^2 = 55 \times 55 = 3025$. This is not 2025.
• Option 4: $65^2 = 65 \times 65 = 4225$. This is not 2025.

Both methods show that 45 multiplied by itself equals 2025.

Conclusion

The square root of 2025 is 45. Therefore, the correct option is 45.