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The Yale Babylonian Collection YBC 7289 clay tablet was created between 1800 BC and 1600 BC, showing and as 1;24,51,10 and 42;25,35 base 60 numbers on a square crossed by two diagonals.
The Rhind Mathematical Papyrus is a copy from 1650 BC of an even earlier work and shows how the Egyptians extracted square roots.
In Ancient India, the knowledge of theoretical and applied aspects of square and square root was at least as old as the Sulba Sutras, dated around 800-500 BC (possibly much earlier). A method for finding very good approximations to the square roots of 2 and 3 are given in the Baudhayana Sulba Sutra. Aryabhata in the Aryabhatiya, has given a method for finding the square root of numbers having many digits.
In the Chinese mathematical work Writings on Reckoning, written between 202 BC and 186 BC during the early Han Dynasty, the square root is approximated by using an "excess and deficiency" method, which says to "...combine the excess and deficiency as the divisor; (taking) the deficiency numerator multiplied by the excess denominator and the excess numerator times the deficiency denominator, combine them as the dividend."
According to historian of mathematics D.E. Smith, Aryabhata's method for finding the square root was first introduced in Europe by Cataneo in 1546.
The symbol for the square root was first used in print in 1525 in Christoph Rudolff's Coss, which was also the first to use the then-new signs '+' and '-'.
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Are all square roots are irrational numbers?
No. The square roots of perfect squares are rational.
How are square roots and perfect squares the same?
They are not.
What are the rules for squares and squares roots?
With square roots if you have a number times itself or squared then that that product is that numbers square root example: 9x9= 81 81 square root is 9
What are examples of perfect square roots?
Perfect square roots are the counting numbers {1, 2, 3, ...} The squares of the perfect square roots are the perfect squares, namely 1² = 1, 2² = 4, 3² = 9, etc.
Why are square roots and perfect squares important?
All numbers are important.
How are square roots and perfect squares related?
The square root of every perfect square is an integer. However, there are also square roots of numbers that are not perfect squares.
What is the relationship between perfect squares and square roots?
The square roots of perfect squares are the numbers that when squared create perfect squares as for example 36 is a perfect square and its square root is 6 which when squared is 36
Are all square roots are irrational numbers?
No. The square roots of perfect squares are rational.
What has integer's as square roots?
perfect squares
How are square roots and perfect squares the same?
They are not.
What are the rules for squares and squares roots?
With square roots if you have a number times itself or squared then that that product is that numbers square root example: 9x9= 81 81 square root is 9
What are examples of perfect square roots?
Perfect square roots are the counting numbers {1, 2, 3, ...} The squares of the perfect square roots are the perfect squares, namely 1² = 1, 2² = 4, 3² = 9, etc.
Numbers whose square roots are integers are called?
perfect squares
What is a number that has large integers as its square roots?
Large perfect squares.
Why are square roots and perfect squares important?
All numbers are important.
What types of numbers have whole number square roots?
They are the perfect squares.
What are numbers with with square roots that are a whole number called?
perfect squares
