# Value Of Root 3 - Long Division Method

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.

## The root of 3 using Long Division:

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.

• First, write 3 as 3.00000000 and group the 0s following the decimal point in pairs of 2 from left to right, as seen below. (Pair the digits to the left of the decimal point from right to left.)
• Consider a number that, when multiplied by itself, is less than or equal to three. In this case, that number is 1 because 2 x 2 = 4.
• Taking 3 by 1 and dividing by 1, we obtain a residual of 2.
• To make the dividend 200, drag a pair of 0s down and fill it next to a 2.
• The divisor, which is 1 in this case, is multiplied by itself and printed below. Now that we have 2K as the new divisor, we must find several K such as the product of 2K. The K is less than or equal to 200. In this example, the necessary value is 27.
• After a decimal place, the number 7 is added to the quotient. In this example, the new divisor for the next division is 2K + K, which is 27 + 7, which equals 34.

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.