Arithmetic Volume 7-8 (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1920 Excerpt: ... as a factor gives us the 2d power of 5, or 25 (5 X 5). 5 used three times as a factor gives us the 3d power of 5, or 125 (5 X 5 X 5). The 2d power of any number is called the "square" of that number; the 3d power is called the "cube" of that number. 5 X 5 = 25, also written 5 square, or 52. 5X5X5 = 125, also written 5 cube, or 53. The small figure telling the power of the number is called the exponent. What exponents were used here? Exercise 18--Oral. 1. Give the areas of the following: Find the values of: . 37, 2.53; 38..122; 39. 1.182; 40. ($)3. Lesson 9 What Roots Are Any one of the equal factors which produce a number is called a "root" of that number; thus a number is the "root" of all of its "powers." The root of a 2d power is called a "square root '; therefore, since 5 X 5 = 25, the square root of 25 is 5. 5 is one of the two equal factors that produce 25. The root of a 3d power is called a "cube root"; therefore, since 5X5X5 = 125, the cube root of 125 is 5. 5 is one of the three equal factors that produce 125. To indicate square root, the symbol y/ called a "radical sign" is used; thus, V25 = 5. A small figure 2 called an "index" is sometimes written in the radical sign to indicate square root; thus, -25 = 5, but this is unnecessary as square root is the simplest form of root, and square root is understood unless some other index is used, as: (a) V25 means square root of 25. Ans., 5. (fe)-vT25 means cube root of 125..Ans., 5. Fxercise 20--Oral. 1. What is the square root of 4? Of 49? Of 144? Of i? 2. What is the cube root of 8? Of 64? Of 27? Of f? 3. If the cube is 8, what is the root from which it came? 4. V36 = 6; explain which is the power. Which is the root? 5.-...