The symbol ‘√’ represents the square root, and it is used to denote the square root of a number. When dealing with perfect square numbers like 4, finding their square roots is straightforward. However, for non-perfect square numbers, the long division method is required to determine their root value.
The square root of 4 is exactly 2. However, it’s important to note that roots can be positive or negative, meaning there are always two roots for any given number. Thus, the square root of 4 can be expressed as ±2 or +2 and -2 (positive 2 and negative 2). Alternatively, you can also use a calculator or an online square root calculator to find the square root of a number.
A square number is obtained when a number is multiplied by itself. For example, 3 multiplied by 3 equals 9, making 9 a square number. Here are some more examples:
16 = 4 x 4 = 4^2
64 = 8 x 8 = 8^2
49 = 7 x 7 = 7^2
36 = 6 x 6 = 6^2
In this article, we will focus on finding the square root of 4. This topic is extensively covered in the Class 8 syllabus, where square numbers and their square roots are explored. Let’s now delve into some basic concepts related to square roots.
What is a perfect square?
Determining whether a number is a perfect square or not can be done using a simple rule:
If a number ends with 2, 3, 7, or 8 in the units place, it is not a perfect square. If a number is a perfect square, it will end with 1, 4, 5, 6, or 9 in the units place. However, the reverse is not always true. For example, 25 is a perfect square, but 35 is not.
What is the square root of 4?
In mathematics, squaring a number is relatively easy as it involves a simple calculation. However, finding the square root of a number can be more challenging, as it requires determining the original number that was squared. For example, both +5 and -5 are square roots of 25 because 5^2 = (-5)^2 = 25. A non-negative real number has a unique non-negative square root, which is called the principal square root and denoted by √a. The symbol √ is known as the radical symbol or radix. In the case of 25, the principal square root is 5, represented as √25 = 5, because 5^2 = 5 x 5 = 25, and 5 is non-negative. The number inside the radical symbol is called the radicand, which in this example is 25.
Applying the same principle, both +2 and -2 are square roots of 4 because 2^2 = (-2)^2 = 4. A non-negative real number also has a unique non-negative square root, known as the principal square root. In this case, the principal square root of 4 is 2, denoted as √4 = 2, because 2^2 = 2 x 2 = 4, and 2 is non-negative. The number inside the radical symbol is the radicand, which is 4 in this example. If you’d like a shortcut method to find the square root of a number, you can refer to a video tutorial for assistance.