Ads
related to: perfect square root worksheets
Search results
Results From The WOW.Com Content Network
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
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.
() is always a perfect square. [10] As it is only a necessary condition but not a sufficient one, it can be used in checking if a given triple of numbers is not a Pythagorean triple. For example, the triples {6, 12, 18} and {1, 8, 9} each pass the test that ( c − a )( c − b )/2 is a perfect square, but neither is a Pythagorean triple.
Leonard Eugene Dickson (1920) [6] attributes to himself the following method for generating Pythagorean triples. To find integer solutions to + =, find positive integers r, s, and t such that = is a perfect square.
In each right triangle, Pythagoras' theorem establishes the length of the hypotenuse in terms of this unit. If a hypotenuse is related to the unit by the square root of a positive integer that is not a perfect square, it is a realization of a length incommensurable with the unit, such as √ 2, √ 3, √ 5 .
The traditional pen-and-paper algorithm for computing the square root is based on working from higher digit places to lower, and as each new digit pick the largest that will still yield a square . If stopping after the one's place, the result computed will be the integer square root.