The square root of 72 is a mathematical operation that determines the value which, when multiplied by itself, gives the result of 72. In other words, it is the number that, when squared, equals 72.
The square root of 72 is approximately 8.485.
The square root of 72 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 72 goes on indefinitely without repeating or terminating.
There are several methods to solve for the square root of 72. Here, we will use the prime factorization method.
Step 1: Find the prime factorization of 72. 72 = 2^3 * 3^2
Step 2: Group the prime factors in pairs. 72 = (2^2 * 3) * (2 * 3)
Step 3: Take one factor from each pair and multiply them. 72 = 2^2 * 3 = 12
Step 4: The square root of 72 is the square root of the product obtained in step 3. √72 = √(2^2 * 3) = 2√3
Example 1: √72 = 2√3
Example 2: √(72/9) = √8 = 2√2
Example 3: √(72 * 2) = √144 = 12
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: rational and irrational. A rational square root is a square root that can be expressed as a fraction or a ratio of two integers. An irrational square root is a square root that cannot be expressed as a fraction or a ratio of two integers.
Q: What is the square root of 72? A: The square root of 72 is approximately 8.485.
Q: Is the square root of 72 a rational number? A: No, the square root of 72 is an irrational number.
Q: How can I calculate the square root of 72? A: You can calculate the square root of 72 using various methods, such as prime factorization or using a calculator.