right and left. In the decimal there are two periods, so there will be two figures in the root decimal. Proceed as before. You will find the trial divisor 300 is not contained in 225, so bring down another period and annex two zeros at the right of the trial divisor. EXAMPLE: Find the cube root of .0163956, carrying the root to 3 decimal places. 1. What is meant by a power of a number? by a root? 2. Give the second and third powers of numbers to 12 by writing results only. 3. State how you find the cube root of a fraction. Cube of the tens + 3 x tens squared multiplied by the units + units squared multiplied by 3 X tens + cube of the units. CUBES GEOMETRICALLY. For graphic illustration the geometrical representation of the cube of units and tens in the drawings is helpful. TO ILLUSTRATE: Find the cube of 12.. EXPLANATION: The cube of (10+2 ) = 103 + 3 ( 102 × 2) + 3 (10 × 22 ) + 28. The cube at the top and to the left may represent une whose edge is 10 in. The illustration to the right of the first may represent the three square solids each 10 in. in length and width, but only 2 in. thick. The next illustration shows the preceding two combined. The fourth illustration shows, first, the three rectangular solids each 10 in. long, but only 2 in. wide, and 2 in. thick; second, the small solid which represents the cube of 2 and is only 2 in. on an edge. The last illustration shows the completed large cube which includes all the others. If any root is to be found higher than the cube root, factor the root figure indicated and use the processes already given. EXAMPLE: 8 6561 = ? The factors of the root figure 8 are 2, 2, 2. Thus, we find the square root of 6561, then the A. H.-27 square root of that result, and then the square root of the third result, which will be the 8th root of 6561. The sixth root is the same as the square root of the cube root. (Find either the square root first or the cube root first.) The 16th root of a number is the same as the square root of the square root of the square root of the square root of that number. |