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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}} .
The adjusted representation will become the equivalent of 31.4159 × 10 2 so that the square root will be √ 31.4159 × 10 1. If the integer part of the adjusted mantissa is taken, there can only be the values 1 to 99, and that could be used as an index into a table of 99 pre-computed square roots to complete the estimate.
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.
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, ...
Substituting 4y 2 for c 2 in the first equation (c 2 = 2b 2) gives us 4y 2 = 2b 2. Dividing by 2 yields 2y 2 = b 2. Since y is an integer, and 2y 2 = b 2, b 2 is divisible by 2, and therefore even. Since b 2 is even, b must be even. We have just shown that both b and c must be even. Hence they have a common factor of 2.
For example, the square root of 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x 2 − 2 = 0. The golden ratio (denoted or ) is another irrational number that is not transcendental, as it is a root of the polynomial equation x 2 − x − 1 = 0.
The square root of 2 is an algebraic number equal to the length of the hypotenuse of a right triangle with legs of length 1. An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational ) coefficients.
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.