what is square route

Square roots" redirects here. For the music festival, seeSquare Roots. For the documentary, seeSquare Roots: The Story of SpongeBob SquarePants.Measured fall time of a small steel sphere falling from various heights. The data is in good agreement with the predicted fall time of, where h is the height and g is the acceleration of gravity.

Inmathematics, asquare rootof a numberais a numberysuch thaty2=a, or, in other words, a numberywhosesquare(the result of multiplying the number by itself, ory×y) isa.[1]For example, 4 and 4 are square roots of 16 because 42= (4)2= 16.

Every non-negativereal numberahas a unique non-negative square root, called theprincipal square root, which is denoted by, where √ is called theradical signorradix. For example, the principal square root of 9 is 3, denoted, because32= 3 × 3 = 9and 3 is non-negative. The term whose root is being considered is known as theradicand. The radicand is the number or expression underneath the radical sign, in this example 9.

Every positive numberahas two square roots:, which is positive, and, which is negative. Together, these two roots are denoted(see± shorthand). Although the principal square root of a positive number is only one of its two square roots, the designation "thesquare root" is often used to refer to theprincipalsquare root. For positivea, the principal square root can also be written inexponentnotation, asa1/2.[2]

Square roots of negative numbers can be discussed within the framework ofcomplex numbers. More generally, square roots can be considered in any context in which a notion of "squaring" of some mathematical objects is defined (includingalgebras of matrices,endomorphism rings, etc.)

Square roots of positivewhole numbersthat are notperfect squaresare alwaysirrational numbers: numbers not expressible as aratioof two integers (that is to say they cannot be written exactly asm/n, wheremandnare integers). This is the theoremEuclid X, 9almost certainly due toTheaetetusdating back to circa 380 BC.[3]The particular caseis assumed to date back earlier to thePythagoreansand is traditionally attributed toHippasus.[citation needed]It is exactly the length of thediagonalof asquarewith side length 1.

Contents[hide]
  • 1Properties
  • 2Computation
  • 3Square roots of negative and complex numbers
    • 3.1Square root of an imaginary number
    • 3.2Principal square root of a complex number
    • 3.3Algebraic formula
    • 3.4Notes
  • 4Square roots of matrices and operators
  • 5Uniqueness of square roots in general rings
  • 6Principal square roots of the positive integers
    • 6.1As decimal expansions
    • 6.2As expansions in other numeral systems
    • 6.3As periodic continued fractions
  • 7Geometric construction of the square root
  • 8History
  • 9See also
  • 10Notes
  • 11References
  • 12External links

  • 1
What are you looking for?