Table of Contents

## Value of root 2

The square root of 2 is expressed as √2 . In exponential; form we can even write it as (2)^½. If we round up √2 upto 10 decimal points we get 1.4142135624.

1.4142135624 is also the solution of the equation x^2=2.

## The value of under root 2

There are three different ways of expressing value of square root 2. The three forms have been stated below.

- Decimal Format = 4142135624.
- In radical format, under root of 2 is expressed as √2
- In exponential form we can write it as (2)^½.

## The value of root 2

Whenever we find the double of a number, we often express it as a square. Now you must be wondering how we express inverse operation of the square. This is where the use of the concept under root comes into play.

A number when multiplies with itself gives us the results as double of the under root, is known as the under root of a number.

Read about table of 4.

## When the value of root 2 discovered?

The under root concept was discovered in earlier times by the Greeks. While they were dividing numbers, they found that few of the numbers could not be divided in p/q form, where q is not equal to 0. The concept later came to be known as under root concept and henceforth it was discovered to be a rational number.

The same under root concept is also used in Pythagoras Theorem, to find the third side of a triangle when two of the other sides are known to us.

## Value of root 2: rational or irrational?

Till now we know the value of √2 till 1 trillion decimal points. So for now, it is considered to be an irrational number.

Read about cos 60.

## Value of root 2: Important Points

The below stated points are few additional information points related to **√**2.

**√**2 is also known as the Pythagoras constant.- It is known to represent diagonal of a one unit square.
- √2 is an irrational number.
- Its decimal is non-terminating and non-repeating.

## How to find the value of root of 2?

Since we have known enough about under root 2, let’s now learn how to find an under root of 2. There are two ways to find an under root of a number. They are

- Long Division Method
- Estimation Method

Read about table of 2

### Value of root of 2 by long division method

Follow the below steps to find the under root of 2 by long division method.

- Find the largest number whose square is less than or equal to the number 2.
- Use the number as quotient and divisor. Divide it to get the remainder.
- In the quotient, put a decimal after 1. Pull down two zeroes to the right of the remainder.
- Double the divisor and leave a blank space on the right of it.
- Find the largest digit so that when the new divisor is multiplied to the quotient the product should be less than or equal to dividend
- Repeat the steps upto desired number of decimal points you want.
- If you follow the steps correctly, the final answer should be 1.4142

### Value of root of 2 by Estimation method

Follow the below steps to find the under root of 2 by estimation method.

- The formula to be used is: y
_{n+1}= ((x/y_{n}) + y_{n})/2. - Repeat the formula upto desired number of decimal points.
- y
_{1}= (2 + 1)/2 = 1.5 - y2= (4/3 + 3/2)/2 = 1.4166 and so on.