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The square root of 2 (approximately 1.4142) is the positive real number that, when multiplied by itself or squared, equals the number 2. It may be written in mathematics as 2 {\displaystyle {\sqrt {2}}} or 2 1 / 2 {\displaystyle 2^{1/2}} .
Notation for the (principal) square root of x. For example, √ 25 = 5, since 25 = 5 ⋅ 5, or 5 2 (5 squared). In mathematics, a square root of a number x is a number y such that =; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x. [1]
The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
Since c 2 = 2b 2, c 2 is divisible by 2, and therefore even. Since c 2 is even, c must be even. Since c is even, dividing c by 2 yields an integer. Let y be this integer (c = 2y). Squaring both sides of c = 2y yields c 2 = (2y) 2, or c 2 = 4y 2. Substituting 4y 2 for c 2 in the first equation (c 2 = 2b 2) gives us 4y 2 = 2b 2. Dividing by 2 ...
Square root of 2, Pythagoras constant. [4] 1.41421 35623 73095 04880 ... where the signs + or − are chosen at random with equal probability 1/2 ...
Hence, a square with side length n has area n 2. If a square number is represented by n points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of n; thus, square numbers are a type of figurate numbers (other examples being cube numbers and triangular numbers).
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The two square roots of a negative number are both imaginary numbers, and the square root symbol refers to the principal square root, the one with a positive imaginary part. For the definition of the principal square root of other complex numbers, see Square root § Principal square root of a complex number.