# Square Root of 20: Everything You Need to Know

The square root of 20 is a mathematical concept that many people find intriguing. It is a non-integer number that can represent the length of the diagonal of a square whose sides measure 20 units. In this article, we will provide you with everything you need to know about the square root of 20.

First, let’s define what a square root is. In mathematics, a square root is a number that, when multiplied by itself, results in the original number. For instance, the square root of 9 is 3 because 3 x 3 = 9. The square root of 20, however, is not an integer, and it cannot be expressed as a simple fraction either. Instead, it is an irrational number, which means it goes on infinitely without repeating.

The exact value of the square root of 20 can be calculated using various methods, including long division, prime factorization, and estimation. One of the most common ways to find the square root of a number without a calculator is by using the prime factorization method. Here’s how it works for 20:

Step 1: Find the prime factors of 20, which are 2 and 5.
Step 2: Pair the prime factors in twos, starting from the left. That gives you 2 x 2 and 5.
Step 3: Multiply the paired factors together and bring them outside the square root sign. That gives you 2 x 2 = 4.
Step 4: If there is an odd number of primes, leave one inside the square root sign. In this case, there is one prime (5) remaining, so it stays inside the square root sign.
Step 5: Combine the terms inside the square root sign. You get √20 = 2√5.

Therefore, the square root of 20 is equal to 2 times the square root of 5.

It is also essential to understand that the square root of 20 is irrational. Irrational numbers cannot be written as fractions because they are non-repeating and do not terminate. In other words, the decimal representation of the square root of 20 goes on infinitely without repeating any pattern. The first few digits of the square root of 20 are 4.472136, but it goes on infinitely from there.

In conclusion, knowing the square root of 20 is useful in various areas of life, including mathematics, science, engineering, and construction. It is a non-integer and irrational number that can be calculated using different methods. The most common technique is prime factorization, which involves composing the number into its prime factors and then multiplying them to get the square root. The square root of 20 is equal to 2 times the square root of 5 and goes on infinitely without repeating. Understanding this concept is crucial to excel in mathematics and other related fields.