Find the square root

(i) 625

(ii) 1225

To find the square roots of the numbers 625 and 1225, we can use a straightforward approach. The square root of a number is a value that, when multiplied by itself, gives the original number. Let's break it down step by step for each number.

Calculating the Square Root of 625

First, let's consider 625. We want to find a number that, when squared, equals 625. One way to approach this is to look for perfect squares. A perfect square is a number that can be expressed as the square of an integer.

Finding Factors

We can start by factoring 625:

• 625 can be divided by 25: 625 ÷ 25 = 25
• Then, 25 can be divided by 5: 25 ÷ 5 = 5
• Finally, 5 is a prime number.

So, we can express 625 as:

625 = 25 × 25 = 5 × 5 × 5 × 5

Finding the Square Root

Since 625 can be expressed as \(5^4\), we can find the square root by taking half of the exponent:

√625 = 5^(4/2) = 5^2 = 25

Thus, the square root of 625 is 25.

Calculating the Square Root of 1225

Now, let's move on to 1225. Again, we are looking for a number that, when multiplied by itself, gives us 1225.

Factoring 1225

We can start by checking if 1225 is divisible by smaller numbers:

• 1225 is divisible by 25: 1225 ÷ 25 = 49
• Next, we can factor 49: 49 = 7 × 7

So, we can express 1225 as:

1225 = 25 × 49 = 5 × 5 × 7 × 7

Finding the Square Root

Since 1225 can be expressed as \(5^2 × 7^2\), we can find the square root by taking half of the exponents:

√1225 = √(5^2 × 7^2) = 5^(2/2) × 7^(2/2) = 5 × 7 = 35

Therefore, the square root of 1225 is 35.

Summary of Results

To summarize:

• The square root of 625 is 25.
• The square root of 1225 is 35.

Understanding how to find square roots through factoring can be very helpful, especially when dealing with larger numbers. If you have any further questions or need clarification, feel free to ask!