Root 2 Value: Calculation Methods and Solved Examples

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.

Long Division Method To find Square Root

Sample Question on Square Root of 2

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

Q1. Explain how many square roots a positive number can have. How are these square roots different?

Q2. Which type of number has an exact square root?

Q3. Which type of number has an approximate square root?

Q4. How can we use perfect squares to estimate a square root, such as √8?

Q5. Which of the following is the square of an odd number?
(a) 256 (b) 361 (c) 144 (d) 400

Q6. Find the value of \(\sqrt({176} + \sqrt{2401})\).

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.

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Last Modified 14-03-2024

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Root 2 Value: Method and Sample Questions