square root of 75

What does square root of 75 mean?

The square root of 75 is a mathematical operation that determines the value which, when multiplied by itself, gives the result of 75. In other words, it is the number that, when squared, equals 75.

What is the answer to square root of 75?

The answer to the square root of 75 is approximately 8.6603.

Is square root of 75 a rational number or an irrational number?

The square root of 75 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 75 goes on indefinitely without repeating or terminating.

To further explain why the square root of 75 is irrational, we can use the prime factorization method. The prime factorization of 75 is 3 * 5^2. Since there is a prime factor (5) with an odd exponent (2), the square root of 75 cannot be simplified to a rational number.

Solving methods for square root of 75

To find the square root of 75, we can use various methods such as:

1. Prime Factorization Method: Express 75 as a product of its prime factors (3 * 5^2). Take the square root of each prime factor and multiply them together. The square root of 75 is √(3 * 5^2) = 5√3.

2. Long Division Method: This method involves long division to find the square root of 75. It is a more time-consuming process but can be used to find an approximation of the square root.

Step-by-step solution for square root of 75

Using the prime factorization method:

1. Express 75 as a product of its prime factors: 75 = 3 * 5^2.
2. Take the square root of each prime factor: √3 * √(5^2).
3. Simplify the square root of 5^2: √3 * 5.
4. Multiply the simplified factors: 5√3.
5. The square root of 75 is 5√3.

Solved examples of square root of 75

Example 1: Find the square root of 75.

Solution: Using the prime factorization method, we have 75 = 3 * 5^2. Taking the square root of each prime factor, we get √3 * √(5^2) = 5√3. Therefore, the square root of 75 is 5√3.

Example 2: Approximate the square root of 75 to the nearest hundredth.

Solution: Using a calculator, we find that the square root of 75 is approximately 8.6603.

Example 3: Simplify √(75/3).

Solution: Simplifying the expression, we have √(25 * 3/3) = √25 = 5.

What does square root mean in mathematics?

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.

Square root formula

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

√x = x^(1/2)

Symbols used to represent square root

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

Types of square roots

There are two types of square roots:

1. Positive square root (√x): This represents the principal square root, which is always positive.

2. Negative square root (-√x): This represents the negative square root, which is the opposite of the positive square root.

FAQs on square root of 75

Q: What is the square root of 75? A: The square root of 75 is approximately 8.6603.

Q: Is the square root of 75 a rational number? A: No, the square root of 75 is an irrational number.

Q: Can the square root of 75 be simplified? A: Yes, the square root of 75 can be simplified as 5√3.

Q: How can I approximate the square root of 75? A: You can use a calculator to approximate the square root of 75 to the desired precision.