Find the square root of 625: √625
The square root of 625 is 25.
To find the square root of 625, follow these steps:
1. Divide the number by any perfect square that is a factor of it. In this case, we can divide 625 by 25, since it is a perfect square.
625 ÷ 25 = 25
2. Take the square root of the perfect square obtained in the previous step. In this case, the square root of 25 is 5.
Therefore, the square root of 625 (√625) is 25.
To find the square root of 625, you can use a calculator or evaluate it manually using a couple of methods. I'll explain both.
Method 1: Using a Calculator
Most calculators have a square root function. Simply enter the number 625, and then press the square root (√) button. The calculator will give you the result. In this case, the square root of 625 is 25.
Method 2: Manual Calculation
To calculate the square root manually, you can use the prime factorization method. Here's the step-by-step process:
Step 1: Prime Factorization
Find the prime factors of 625. In this case, 625 is a perfect square, so its prime factors are all the prime numbers up to the square root of 625 – 5.
Step 2: Pairing Factors
Pair the prime factors in pairs, starting from the smallest and moving towards the largest. In this case, we have 5 pairs of 5, since 5 is the only prime factor.
Step 3: Simplifying
Take one number from each pair and multiply them together. In this case, we have one 5 left, so we take it.
Step 4: Final Answer
The product of the numbers left after simplifying is the square root of the original number. In this case, the square root of 625 is 25, since 5 × 5 = 25.
Therefore, the square root of 625 is 25.