Square Root Of Negative 2

Foursquare Root of 2

The square root of 2 is expressed equally √2 in the radical form and equally (two)^½ or (2)^0.5 in the exponent form. The foursquare root of two rounded upwards to 10 decimal places is 1.4142135624. It is the positive solution of the equation x² = ii.

Square Root of ii: 1.4142135623730951
Square Root of 2 in exponential class: (2)^½ or (2)^0.5
Square Root of 2 in radical form: √2

1.	What Is the Square Root of 2?
2.	Is Square Root of ii Rational or Irrational?
3.	Important Notes on Square Root of 2
four.	How to Detect the Square Root of two?
5.	Thinking Out of the Box!
6.	FAQs on Square Root of 2

What Is the Square Root of two?

Square root is simply an inverse performance of foursquare. The foursquare root of ii is represented as √ii. This is a number which when multiplied to itself gives us the result as 2. During aboriginal times, Greeks found a number that can never ever be written in the form of p/q, where p,q are integers and q is not equal to 0. This means √ii is non rational.√2 happens to be very useful in geometry. Let'due south say we have a foursquare with side length 1 and you lot want to find the length of the diagonal.

To discover the third side we apply Pythagoras Theorem. The 3rd side will be√2. Let'south locate the number√twoon a number line. Nosotros will use transfer the square we used to discover √two. Let'south proper noun the vertices of the square equally shown. Keep the vertex O at 0. Nosotros already discovered that OB=√ii

Using a compass with centre O and radius OB, describe an arc intersecting the number line at the point P.

The point P corresponds to√2 on the number line.

Is the Square Root of 2 Rational or Irrational?

The bodily value of√2. is undetermined. The value of√2 upto 25 decimal places is 1.4142135623730950488016887..
At present, the value of √ii is known up to 1 trillion decimal place.
Hence,√2 is irrational.

Important Notes:

√2 is too called Pythagoras' constant.
√2 represents the diagonal of a unit foursquare.
√two was the first number to be discovered as an irrational number.
Its decimal representation is non-terminating and non-repeating.
The ratio of longer border and shorter edge of an A4 size canvas paper is equal to √ii.

How to Find the Square Root of two?

We tin find the square root of 2 by the following two methods:

Long Division Method
Estimation and Approximation Method

Square Root of 2 past Long Sectionalisation Method

The value of square root of 2 by long division method consists of following steps:

Step one: Observe the largest number whose square is less than or equal to the number 2. Accept this number as the divisor and the caliber, (1 in this case). Divide and write the remainder.
Step 2: In the quotient, put a decimal point after 1. Bring down 2 zeroes to the right of the remainder. So, the new dividend is 100
Step three:Double the divisor and enter it with a bare on its right. Estimate a largest possible digit to fill the blank which will likewise go the new digit in the quotient, such that when the new divisor is multiplied to the new caliber the product is less than or equal to the dividend. Divide and write the remainder. Echo this process to get the decimal places you desire.

Square Root of two past Estimation and Approximation Method

Nosotros can use the formula y=√x to find the value of√two.

This formula tin be written as

((x/y)+y)/two

The iteration formula is

y_{due north+1} = ((x/y_n) + y_n)/2

The first three iterations give the upshot every bit shown below.Outset set y_ane=1

Iteration 1: y₁ = (2 + 1)/ii = 1.5
Iteration 2: y₂ = (4/three + three/2)/2 = 1.4166
Iteration 3: y_iii= (24/17 + 17/12)/2 = 1.414215...

Have you noticed that information technology has somewhat starting to shape into √two =ane.41421356237309 ?

Explore Foursquare roots using illustrations and interactive examples

Foursquare Root of i
Foursquare Root of 11
Square Root of 5
Square Root of ix
Square Root of 8

Call back Tank:

Tin you remember of any quadratic equation which has a root as √2?
Since (-√two)²=2, tin can we say that -√2 is also a square root of ii?

Square Root of 2 Solved Examples

Example 1: Find the length of diagonal of a square fabricated upward of iv unit squares.

Solution

We know that the length of diagonal of 1 unit of measurement square is√2 units. To find the diagonal, we need to consider the length of diagonal of two unit of measurement squares.
Diagonal of i unit square =√2 units
Sum of Diagonal of 2 unit squares = ii√2 units
Hence, length of diagonal is 2√2 units.
Example two: What would be the length of the diagonal of a square shape cake, if each side is of 2 units? (Write your respond in decimal form upto 3 decimal places)

Solution

Given, Side of the Foursquare Cake = 2 units
Using Pythagoras Theorem,
Diagonalof a square =√2a
Diagonal = √2 × 2 = 2.828 units
Example: If the expanse of an equilateral triangle is 2√3 in². Find the length of 1 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 = (√iii/4)aⁱⁱ = 2√3 in²
⇒ a = ±√8 in
Since length can't exist negative,
⇒ a = √8 = 2 √two
We know that the foursquare root of 2 is i.414.
⇒ a = two.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 i.41421.

Why is the Square Root of ii an Irrational Number?

The number 2 is prime. This implies that the number 2 is pairless and is non in the power of two. Therefore, the square root of 2 is irrational.

If the Square Root of ii is one.414. Notice the Value of the Square Root of 0.02.

Allow u.s.a. correspond √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 Foursquare?

The number two is prime. This implies that the square root of 2 cannot exist 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 foursquare root of -ii is an imaginary number. It can be written as √-2 = √-one × √2 = i √2 = 1.414i
where i = √-1 and information technology is called the imaginary unit.

What is the Value of 17 square root ii?

The foursquare root of ii is i.414. Therefore, 17 √2 = 17 × i.414 = 24.042.