What Is the Square of a Number?
Any number when multiplied by itself results in the square of that number. For example, 12 multiplied by itself results in 144. The number 144 is the square of the number 12. In general finding the square of a number is represented by the equation,
\(x = y^{2}\)– in which x represents the square, and y represents the number being squared. Notice that the exponent of y is 2.
There are also two different types of square numbers, perfect and imperfect. A perfect square number such as 225 gives 15 as its square root. Notice that there are no fractions or decimals that are linked with the square root of perfect square numbers.
What Is the Square Root of a Number?
Now that we know about the square of a number, let us explore the square root of a number. The square root of a number is represented as,
\(\sqrt{x} = y,\) this is taking into consideration the previous equation, \(x = y^{2}.\)
Observe that there is a specific symbol that is used in the equation.
So in the expression, \(\sqrt{x}\) the symbol, \(‘\sqrt{ }’\) is called the radical and the the letter ‘x’ is called the radicand. It must be noted that every perfect square such as 4,25,100, and so on, have two square roots, a positive and a negative square root.
For example, \(\sqrt{255} = +\text{ }15\text{ }or \text{ }- 15.\)
The square root of a number is found by using the long division method, which will be discussed in a related article.
[Note:There are also two different types of square numbers, perfect and imperfect. A perfect square number such as 225 gives 15 as its square root. Notice that there are no fractions or decimals that are linked with the square root of a perfect square. But a number such as 26 is an imperfect square as its square root is 5.099, and the value of the square root has decimal, 0.099 linked to it.]
List of Square Roots from 1–50
As a quick reference guide, students can use this chart to quickly find the square roots of numbers ranging from one to fifty.
Rapid Recall
The square root symbol is called a ‘radical’. The value written under this symbol is known as the ‘radicand’.
Yes, just like squares, a number multiplied by itself for three times results in the cube of the number, and the cube root of the resulting product (cube) gives the original number as the solution. So, 343 is the cube of 7, and the cube root of 343 gives 7 as the cube root.
The history of calculating square roots dates back to thousands of years starting from the Babylonian civilization over 4000 years ago.