Multiplication of Square Roots
Care must be used in multiplying square roots of negative numbers. For example, the following reasoning is incorrect:
The fallacy is that the rule, where the principal value of the square root is taken in each instance, is generally valid only if at least one of the two numbers x or y is positive, which is not the case here.
Read more about this topic: Imaginary Number
Famous quotes containing the words multiplication of, square and/or roots:
“Civilization is a limitless multiplication of unnecessary necessaries.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“If magistrates had true justice, and if physicians had the true art of healing, they would have no occasion for square caps; the majesty of these sciences would of itself be venerable enough. But having only imaginary knowledge, they must employ those silly tools that strike the imagination with which they have to deal; and thereby, in fact, they inspire respect.”
—Blaise Pascal (1623–1662)
“Though of erect nature, man is far above the plants. For man’s superior part, his head, is turned toward the superior part of the world, and his inferior part is turned toward the inferior world; and therefore he is perfectly disposed as to the general situation of his body. Plants have the superior part turned towards the lower world, since their roots correspond to the mouth, and their inferior parts towards the upper world.”
—Thomas Aquinas (c. 1225–1274)