Solving for the Square Root of 125

The square root of 125 is a mathematical problem that requires solving. To solve this problem, we need to understand some fundamental concepts of mathematics, including prime factors, exponents, and the properties of square roots.

Before we start solving the problem, let’s have a brief overview of what a square root is. A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 64 is 8 because 8 multiplied by 8 is 64. The symbol used for square root is √.

Now, let’s move on to solving for the square root of 125. First, we need to determine the prime factors of 125. Prime factors are unique prime numbers that multiply together to form the original number. In other words, they are the building blocks of a number. The prime factors of 125 are 5 and 5 and 5, because 5 multiplied by 5 multiplied by 5 is equal to 125.

Next, we need to express 125 in exponential form. Exponential form is a shorthand way of writing a number as a base raised to a power. We can write 125 as 5 raised to the power of 3 (5³), since we have three 5s multiplying each other to equal 125.

Now that we know the prime factors and exponential form of 125, we can use the properties of square roots to solve for the square root of 125. One important property of square roots is that they can be simplified by dividing the exponent by 2. For example, the square root of 64 can be simplified as the square root of 8², which equals 8. The exponent of 2 is divided by 2 to give us 1, which is the final answer.

Using the same property, we can simplify the square root of 125 as the square root of 5³. To divide the exponent by 2, we can use the rule that says we can pull out pairs of factors from under the radical sign. In this case, we pull out a pair of 5s, leaving one 5 under the radical sign. We now have simplified the original expression, and the square root of 125 can be written as 5√5.

In summary, solving for the square root of 125 required us to understand prime factors and exponents and use the properties of square roots. We started by finding the prime factors of 125, which were 5, 5, and 5. Then, we expressed 125 in exponential form as 5³. Lastly, we used the property of square roots to simplify the expression and get the final answer of 5√5.

Solving mathematical problems is all about understanding the concepts and applying them correctly. The more we practice, the better we become at solving these problems. Next time you come across a square root problem, remember the steps we followed to solve for the square root of 125, and you’ll be on your way to finding the solution.