The root of a number is the counter of squaring a number. If k is the square root of l, then k x k equals l. The ‘√' sign represents the square root. This is known as the radical sign, and the word (integer) contained within it is known as the radicand. In the terminology of exponents, the square root is regarded as an integer raised to the power of ‘1/2'. If x is any positive integer, then the square root is (x 1/2 ).
The root of three can be expressed as √3 in radical form or (3) 0.5 or (3) 1/2 , in exponential form. Since three is not a perfect square, we shall get a decimal value for the root of 3. If we multiply root three twice, we get the whole number three. But what is the number which, when multiplied, yields the root of 3 as a result? Let us find out. It is extremely hard to find the value of root 3, but if we use the long division method, we can effortlessly calculate the approximate value of root 3 in less time.
We can only use the long-division approach to compute the value of the square root of 3 since we know it is non-terminating.
Continuing in the same method and starting from step 4, we can compute the remaining decimals. After applying the long division method, we get the decimal value of root 3 = 1.732. Thus, the long division method is the most successful method for calculating the roots of not perfect squares. After successive iterations using the long division method, we find out that the value of root three continues to √3 = 1.732050807………and so on. This indicates that the value after the decimal point is non-terminating and continues till eternity. Therefore, we can conclude that √3 is an irrational number. Therefore, the roots of √3 are 1.732 and -1.732.