How to find square root of 2 by division method

• Written By Vaibhav_Raj_Asthana
• Last Modified 10-11-2022

Root 2 Value is the value of root 2 or the square root of 2 or sqrt 2 or √2 is 1.414. The square root of 2 or root 2 is represented using the square root symbol √ and will be mentioned as √2. It is an irrational number and cannot be represented in the form of \(\frac{x}{y}\) and just like the value of pi (π), it has infinite numbers after the decimal. Hence for the calculation, we use the approximate value of the square root 2. The square root is an inverse operation of the square. The exact value of root 2 cannot be determined. 

Mathematics is an important subject which students generally find tough to crack. But with regular practice and reading, students can master the subject. Read this article to learn how to calculate square root of 2.

Root 2 Value Calculation

Any root value when multiplied by itself gives the number that is under the root symbol. For example, √5 x √5 = 5 or √44 x √44 = 44, similarly, √2 x √2 = 2. Some important points on the square root are given below:

• i) A square root of a number n is a number m which, when multiplied by itself, equals n.
• ii) The square roots of 36 are 6 and – 6 because 62 = 36 and (– 6)2 = 36.
• iii) If m2 = n, then m is a square root of n.

Value of root 2 up to 50 decimal places

√2 = 1.41421356237309504880168872420969807856967187537694…

How To Find Root 2 Value?

Students can easily find the value of sqrt of a number if that number is a perfect square. Example: The value of √4 is 2 as 4 is a perfect square of 2, and the value of √625 is 25 as 25 x 25 = 625. So, finding √ of a perfect square is easy.

The challenge is to find the square root of not perfect square numbers. For numbers that are not a perfect square, we use the long division method.

Value of Square Root of 2 by Long Division Method

The long division method is the universal way to find out the root of any number irrespective of its type. Through this section we will explain the long division method in step by step:

• 1st Step: Put a bar over e Put a bar over each pair of digits starting from one’s place. If the number of digits in it is odd, then the left-most digit too will have a bar.
• 2nd Step: Check the largest number whose square is ≥ the number under the extreme left bar. Take the no. as the new divisor and the quotient with the number that is under the extreme left as the dividend and Divide to get the next remainder.
• 3rd Step: Bring down the number under the next bar to the right of the remainder.
• 4th Step: Double the quotient and enter it with a blank on its right.
• 5th Step: Repeat steps 2, 3, 4 till the remainder is 0 or is repetitive.
• 6th Step: The quotient will be the square root value.

Here are some questions that will aid students in their preparation:

Q.1: What is the value of the square root of 2?

Ans: Square root 2 equals 1.414.

Q.2: How to calculate square root value using the long division method?

Ans: We have provided the detailed step-by-step process on this page. You can follow these steps to find the square root of any number.

Q.3: Why is √ 2 an irrational number?

Ans: Since √ 2 is not an integer, when we find the value of √ 2 the numbers after the decimal point tend to infinity, it is irrational.

Q.4: What is the value of one divided by root 2?

Ans: The value of one by root 2 is 0.707.

Q.5: Can a number have 2 square roots?

Ans: Every number except 0 has two square roots, a positive and a negative.

Square root of 2 can be calculated as Square root of any other number. The square root of a number is a positive algebraic expression represented by the symbol ‘√‘ and is written as √x or x½. Square root of 2 is an irrational number represented as √2 or 2½. It when multiplied by itself, will result in the number 2. The value of this expression i.e. √2 is 1.414… Its value can’t be determined exactly because it can not be represented as a fraction i.e. in the form of a/b where a and b are integers and b can’t be zero. So, Square root of 2 is considered an irrational number.

Similarly, Is π an irrational number? can be found here.

The value of Square root of 2 is widely used in mathematics as 1.414 because it contains an infinite number of decimals. Hence, to make mathematical computations easy, we use only 3 digits after decimal places. Sometimes 99/70 is also used as a value for Square root of 2. 

Computing Square Roots

The square root of a number is the value that when multiplied by itself, results in the number taken as input. To compute the square root, we first need to check if the number is a perfect square. Perfect Squares are the numbers, the roots of which are whole numbers. For example, 4, 9, 25, 36, 49, etc. It is easier to compute the square root of a perfect square number as compared to a non-perfect square number. To compute the root of a non-perfect number, we need to apply the formula of the long division method.

To compute the square root of a number using the long division method, go through the steps given below: 

Step 1: First we need to divide the number into groups of two starting from right to left.

For example: To compute the value of √132496, we divide the digits into groups like 13, 24, and 96.

Step 2: Now we need to find the highest number that when multiplied by itself results in the number less than or equal to the first pair of digits.

Here, we need a number that when multiplied by itself results in a product ≤ 13. So, the highest number that can be selected is 3.

Step 3: Now compute the remainder and then write the next pair of digits next to the remainder. This will become our dividend for the next step. 

Step 4: To create the divisor, first we will multiply the quotient by 2 and write the product as the digit for the tens place of the divisor. For the unit’s place, we will again perform Step 2.

Step 5: Now perform Step 3 and Step 4 again and then again repeat Step 2 to create the divisor. Continue the same until the remainder becomes zero. 

The quotient formed will be the square root of the number.

Read More

• What are irrational numbers
• Real Numbers

How to Find Square Root of 2?

It is always easier to compute the square root of perfect squares but to compute the square root of a non-perfect square, we need to perform the long division method. To compute the square root of 2, we need to follow the steps given below:

Step 1: Write 2 as 2.000000 to make it easier to divide

Step 2: Now look for the perfect square less than 2 i.e. 1 and divide the number with it.

Step 3: Now the quotient and the remainder are 1. We will place a decimal in the quotient and bring down the pair of zeroes for further division.

Step 4: Now add the quotient with the existing divisor, this will become the digit at the tens place for our next divisor. 

Step 5: For the unit’s place, we need to find a value that can be placed at the unit place of both quotient and the divisor such that the new divisor when multiplied with the unit digit of the quotient results in the highest number less than the remainder. 

Now. bring down the next pair of zeros and repeat the steps 4th and 5th. This can be done for infinite steps as the exact value of the square root of 2 goes up to infinite decimal places. We can compute the result up to 4 decimal places as that can be used for approx. value of the square root.

FAQs on Square Root of 2

Question 1: Why is the Square Root of 2 an Irrational Number?

Answer:

2 is a prime number which signifies that pair of 2 does not exist. i.e. √2 can never be written in the form of p/q. Therefore, square root of 2 is irrational.

Question 2: Is the number 2 a Perfect Square?

Answer:

2 is a prime number this implies that the square root of 2 cannot be expressed as a product of two equal integers. Therefore, 2 is not a perfect square.

Question 3: Is 1.414 the exact value of √2?

Answer:

√2 is an irrational number so it cannot be expressed in the form of a proper decimal number. The value of √2 is a non-terminating decimal which is given as 

√2 = 1.41421356237309504880168872420969807856967187537694…

 But for the sake of calculation, it is taken as 1.414

Question 4: What is the value of √3?

Answer:

√3 is an irrational number so its exact value is never determined. But it can be approximated to √3 = 1.732(approx)