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Value of root 5 - Definition, Examples and Root of 5 Using Long Division


The square root of a number is defined as the converse process of squaring that number. For example, if 7 is the square root of a number, then 7 x 7 = 49 is the square from which the square root has been determined. Square is commonly denoted with the ‘√' sign, which is well known as the radical symbol, and radicand is the term (integer) contained within it. When raised to the power of 0.5 or ‘1/2’, the integer produces the square root. This is known as the exponential form of the root. If ‘c’ is any whole number, then the root of c is (c1/2).

In this article, we shall learn the ways and determine the value of root 5. In the radical form, the root of 5 is represented as √5; if you prefer the exponential form, then you can express it as (5)0.5 or (5)1/2. We will receive a decimal number for the root of 5 since five is not a perfect square. The value of root 5 is incredibly difficult to determine, but if we apply the long division technique, we can easily compute the estimated value of root 5.

The Root of 5 Using Long Division:

Let us utilize the long-division approach to determine the magnitude of the square root of 5 since we can concur that it is non-terminating.

  • Initially, we write five as 5.00000000 and group the 0s in a pair of two from right to left. Thus, ‘5’ will remain unpaired.
  • Our fast task is to find a number whose square is less than 5; in this case, it will be the number 2 as the square of 2 is 4.
  • After dividing 5 with the square of 2, we are left with the remainder 1. So, the first quotient is 2. Now we must drag the first pair of zeros down and add a decimal point to the quotient.
  • Next, we add 2 and the quotient (which is also 2) and now find a number 4K which will divide the number 100 and give us the first value after the decimal. K is the value that will yield a number less than 100 and become the quotient after the decimal.
  • For the root of five, K is 2. 42 x 2 = 84, which is smaller than 100. So we are left with the remainder 16; we drag another pair of zeros to make the number 1600.
  • Now we add 42 + 2 = 44 and have to determine a 3-digit number 44L where L is the number which on multiplication gives a number less than 1600.

In this manner, we shall calculate the approximate value of root 5. After applying the long division method, we get the decimal value of root 5 = 2.2360. The long division method is the most successful method for calculating the roots of numbers that are not perfect squares. After successive iterations using the long division method, we find out that the value of root three continues to √5 = 2.2360………and so on. This indicates that the numbers after the decimal point are non-terminating and extend to infinity. Therefore, we can concur that √5 is an irrational number.

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