NOVEMBER 08, 2023

The square root of 125 is a mathematical operation that determines a number which, when multiplied by itself, equals 125. In other words, it finds the value that, when squared, gives the result of 125.

The answer to the square root of 125 is approximately 11.18034.

The square root of 125 is an irrational number. An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers. The decimal representation of the square root of 125 goes on indefinitely without repeating or terminating, indicating its irrationality.

There are several methods to solve for the square root of 125. Here, we will use the most common method, which is the long division method.

Step-by-step solution:

- Start by assuming a number, let's say x, as the square root of 125.
- Divide 125 by x.
- Take the average of x and the result of the division in step 2.
- Repeat steps 2 and 3 until you reach a desired level of accuracy.

Using this method, we can find that the square root of 125 is approximately 11.18034.

Example 1: Find the square root of 125.

Solution: Using the long division method, we assume x = 10 as the initial approximation. 125 divided by 10 equals 12.5. The average of 10 and 12.5 is 11.25. 125 divided by 11.25 equals 11.1111. The average of 11.25 and 11.1111 is 11.18056. Continuing this process, we can approximate the square root of 125 as 11.18034.

Example 2: Evaluate √125 + √125.

Solution: √125 + √125 = 11.18034 + 11.18034 = 22.36068.

Example 3: Simplify √(125/5).

Solution: √(125/5) = √25 = 5.

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √ and is used to find the side length of a square with a given area or to solve quadratic equations.

The square root of a number x can be calculated using the formula:

√x = x^(1/2)

The symbol √ is used to represent the square root in mathematics.

There are two types of square roots: positive square roots and negative square roots. The positive square root represents the principal square root, while the negative square root represents the opposite value.

Q: What is the square root of 125? A: The square root of 125 is approximately 11.18034.

Q: Is the square root of 125 a rational number? A: No, the square root of 125 is an irrational number.

Q: How can I calculate the square root of 125? A: You can use the long division method or a calculator to calculate the square root of 125.

Q: What is the square root of 125 squared? A: The square root of 125 squared is equal to 125.