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The radical symbol refers to the principal value of the square root function called the principal square root, which is the positive one. 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 ...
The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors. Since p 2 k = p k , {\textstyle {\sqrt {p^{2k}}}=p^{k},} only roots of those primes having an odd power in the factorization are necessary.
A square root of a number x is a number r which, when squared, becomes x: =. Every positive real number has two square roots, one positive and one negative. For example, the two square roots of 25 are 5 and −5. The positive square root is also known as the principal square root, and is denoted with a radical sign:
√ (square-root symbol) Denotes square root and is read as the square root of. Rarely used in modern mathematics without a horizontal bar delimiting the width of its argument (see the next item). For example, √2. √ (radical symbol) 1. Denotes square root and is read as the square root of.
Square root of 2, Pythagoras constant [4] 1.41421 35623 73095 04880 [Mw 2] [OEIS 3] Positive root of = 1800 to 1600 BCE [5] Square root of 3, Theodorus' constant [6] 1.73205 08075 68877 29352 [Mw 3] [OEIS 4] Positive root of = 465 to 398 BCE
radical symbol (for square root) 1637 (with the vinculum above the radicand) René Descartes (La Géométrie) % percent sign: 1650 (approx.) unknown
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}} .
The square root of 2 is equal to the length of the hypotenuse of a right-angled triangle with legs of length 1. The square root of 2, often known as root 2 or Pythagoras' constant, and written as √ 2, is the unique positive real number that, when multiplied by itself, gives the number 2.