The square root of 2 is expressed as √2 in the radical form and as (2)½ or (2)0.5 in the exponent form. The square root of 2 rounded up to 10 decimal places is 1.4142135624. It is the positive solution of the equation x2 = 2.
- Square Root of 2: 1.4142135623730951
- Square Root of 2 in exponential form: (2)½ or (2)0.5
- Square Root of 2 in radical form: √2
| 1. | What Is the Square Root of 2? |
| 2. | IsSquare Root of 2 Rational or Irrational? |
| 3. | Important Notes on Square Root of 2 |
| 4. | How to Find the Square Root of 2? |
| 5. | Thinking Out of the Box! |
| 6. | FAQs on Square Root of 2 |
What Is the Square Root of 2?
Square rootis just an inverse operation of square. The square root of 2 is represented as √2.This is a number which when multiplied to itself gives us the result as 2. During ancient times, Greeks found a number that can never ever be written in the form of p/q, where p,q are integersand q is not equal to 0. This means √2 is not rational.√2 happens to be very useful in geometry. Let's say wehave a square with side length 1 and you want to find the length of the diagonal.
To find the third side weuse Pythagoras Theorem. The third side will be√2. Let's locate the number√2on a number line. We will usetransfer the square we used to discover √2. Let's name the vertices of the square as shown. Keep the vertex Oat 0. We already discovered that OB=√2
Using a compass with centre Oand radius OB, draw an arc intersecting the number line at the point P.
The point Pcorresponds to√2on the number line.
Is the Square Root of 2Rational orIrrational?
The actual value of√2. is undetermined. The value of√2upto 25 decimal places is 1.4142135623730950488016887..
At present, the value of √2 is known up to 1 trillion decimal place.
Hence,√2 is irrational.
Important Notes:
- √2 is also calledPythagoras' constant.
- √2 represents the diagonal of a unit square.
- √2 was the first number to be discovered as an irrational number.
- Its decimal representation is non-terminating and non-repeating.
- The ratio of longer edge and shorter edge of an A4 size sheet paper is equal to √2.
How to Find the Square Root of 2?
We can find the square root of 2 by the following two methods:
- Long Division Method
- Estimation and Approximation Method
Square Root of 2by Long Division Method
The value of square root of 2 by long division method consists of following steps:
- Step 1: Find the largest number whose square is less than or equal to the number 2.Take this number as the divisor and the quotient, (1 in this case). Divide and writethe remainder.
- Step 2: In the quotient, put a decimal point after 1. Bring down two zeroesto the right of the remainder. So, the new dividend is 100
- Step 3:Double the divisor and enter it with a blank on its right.Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend.Divide and writethe remainder.Repeat this process to get the decimal places you want.
Square Root of 2by Estimation and Approximation Method
We can use the formula y=√xto find the value of√2.
This formula can be written as
((x/y)+y)/2
The iteration formula is
yn+1= ((x/yn) +yn)/2
The first three iterations givethe result as shown below.First set y1=1
- Iteration 1:y1= (2+ 1)/2 = 1.5
- Iteration 2:y2= (4/3+ 3/2)/2 = 1.4166
- Iteration 3:y3= (24/17+ 17/12)/2 = 1.414215...
Have you noticed that it has somewhat starting to shape into √2 =1.41421356237309 ?
Explore Square roots using illustrations and interactive examples
- Square Root of 1
- Square Root of 11
- Square Root of 5
- Square Root of 9
- Square Root of 8
Think Tank:
- Can you think of any quadratic equation which has a root as √2?
- Since (-√2)2=2, can we say that -√2 is also a square root of 2?
Square Root of 2 Solved Examples
Example 1: Find the length of diagonal of a square made up of 4 unit squares.
Solution
We know that the length of diagonal of 1 unit square is√2 units. To find the diagonal, we need to consider the length of diagonal of 2 unit squares.
Diagonal of 1 unit square =√2 units
Sum of Diagonal of 2 unit squares =2√2 units
Hence, length of diagonal is2√2 units.Example 2: What would be the length of the diagonal of a square shape cake, if each side is of 2units? (Write your answer in decimal form upto 3 decimal places)
Solution
Given, Side of the Square Cake = 2units
Using Pythagoras Theorem,
Diagonalof a square =√2a
Diagonal=√2×2 = 2.828 unitsExample: If the area of an equilateral triangle is 2√3 in2. Find the length of one of the sides of the triangle.
Solution:
Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a2 = 2√3 in2
⇒ a = ±√8 in
Since length can't be negative,
⇒ a = √8 = 2 √2
We know that the square root of 2 is 1.414.
⇒ a = 2.828 in
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FAQs on the Square Root of 2
What is the Value of the Square Root of 2?
The square root of 2 is 1.41421.
Why is the Square Root of 2 an Irrational Number?
The number 2 is prime. This implies that the number 2 is pairless and is not in the power of 2. Therefore, the square root of 2 is irrational.
If the Square Root of 2 is 1.414. Find the Value of the Square Root of 0.02.
Let us represent √0.02 in p/q form i.e. √(2/100) = 0.02/10 = 0.141. Hence, the value of √0.02 = 0.141
Is the number 2 a Perfect Square?
The number 2 is prime. This implies that the square root of 2 cannot be expressed as a product of two equal integers. Therefore, the number 2 is not a perfect square.
What is the Square Root of -2?
The square root of -2 is an imaginary number. It can be written as √-2 = √-1 × √2 = i √2 = 1.414i
where i = √-1 and it is called the imaginary unit.
What is the Value of 17 square root 2?
The square root of 2 is 1.414. Therefore, 17 √2 = 17 × 1.414 = 24.042.
