What is the square root of 1

The square root is an inverse mathematical operation of a square. As you are aware, exceptional cases are always there. In mathematics, there are too many exceptions we deal with. Look at the multiplication shown below when 1 is multiplied by 1 we get a new number as 1, 1 is a square root of 1, or square of 1 is also 1.

The square root of 1 refers to the value which when multiplied by itself gives the result as 1. For 1, its square root can be either 1 or -1 as both 1 multiplied by 1 and -1 multiplied by -1 gives the result as 1. In general, every number has two square roots, i. In general, when talking about square roots , only the positive square root is considered i. As 1 is a real number and the square of any number is positive, we can assume that the square root of 1 is 1 itself. Representing this mathematically we get the following:.

What is the square root of 1

Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers , using addition and multiplication. Here, the term "imaginary" is used because there is no real number having a negative square. In contexts in which use of the letter i is ambiguous or problematic, the letter j is sometimes used instead. For example, in electrical engineering and control systems engineering , the imaginary unit is normally denoted by j instead of i , because i is commonly used to denote electric current. Square roots of negative numbers are called imaginary because in early-modern mathematics , only what are now called real numbers , obtainable by physical measurements or basic arithmetic, were considered to be numbers at all — even negative numbers were treated with skepticism — so the square root of a negative number was previously considered undefined or nonsensical. A unit is an undivided whole, and unity or the unit number is the number one 1. Although the construction is called "imaginary", and although the concept of an imaginary number may be intuitively more difficult to grasp than that of a real number, the construction is valid from a mathematical standpoint. In the complex plane , which is a special interpretation of a Cartesian plane , i is the point located one unit from the origin along the imaginary axis which is orthogonal to the real axis. Although the two solutions are distinct numbers, their properties are indistinguishable; there is no property that one has that the other does not. For more on this general phenomenon, see Galois group. Using the concepts of matrices and matrix multiplication , complex numbers can be represented in linear algebra.

So based on this property of the radical of the principal root, they'll say that this over here is the same thing as the square root of negative 1 times negative 1.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Search for courses, skills, and videos. The imaginary unit i. About About this video Transcript. The video explores the intriguing concept of imaginary numbers, specifically the imaginary unit 'i'.

The square root is an inverse mathematical operation of a square. As you are aware, exceptional cases are always there. In mathematics, there are too many exceptions we deal with. Look at the multiplication shown below when 1 is multiplied by 1 we get a new number as 1, 1 is a square root of 1, or square of 1 is also 1. This is an exceptional case of a square root of 1. Hence, the square root of 1 is rational. There are multiple ways to find square roots. Here you will be learning about the long division method. The value of the square root of 1 by the long division method consists of the following steps. The first step is to think about the number whose square is less than or equal to the number 1, treat this number as the divisor as well as the quotient 1 in this case.

What is the square root of 1

Use this calculator to find the principal square root and roots of real numbers. Inputs for the radicand x can be positive or negative real numbers. The answer will also tell you if you entered a perfect square. The answer will show you the complex or imaginary solutions for square roots of negative real numbers.

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Commercial Maths. Privacy Policy. In the applied area of Mathematics, the concept of square roots is considered to be highly important. Start Quiz. Toggle limited content width. Already booked a tutor? When the imaginary unit is repeatedly added or subtracted, the result is some integer times the imaginary unit, an imaginary integer ; any such numbers can be added and the result is also an imaginary integer:. However, great care needs to be taken when manipulating formulas involving radicals. Downvote Button navigates to signup page. In other words the square root of -1 is not a real number. Posted 13 years ago. About About this video Transcript.

Our square root calculator estimates the square root of any positive number you want.

The imaginary unit i. Brian Lee. And then they would tell you that, hey, look just from straight up properties of the principal square root function, they'll tell you that the square root of a times b is the same thing as the principal square root of a times the principal square root of b. The concept lays the basic foundation for algebra. Posted 10 years ago. They are:. When taking square roots of a positive number you always get two answers. Graph will be Uploaded soon. Posted 7 years ago. Although the construction is called "imaginary", and although the concept of an imaginary number may be intuitively more difficult to grasp than that of a real number, the construction is valid from a mathematical standpoint. And they'll argue therefore, you can't make this substitution that we did in this step. A unit is an undivided whole, and unity or the unit number is the number one 1. Categories : Complex numbers Algebraic numbers Quadratic irrational numbers Mathematical constants.