Square Roots and Cube Roots | cube root symbol
Tofindthecuberootofanumber,youwanttofindsomenumberthatwhenmultipliedbyitselftwicegivesyoutheoriginalnumber.Inotherwords,tofindthecuberootof8,youwanttofindthenumberthatwhenmultipliedbyitselftwicegivesyou8.Thecuberootof8,then,is2,because2×2×2=8.Noticethatthesymbolforcuberootistheradicalsignwithasmallthree(calledtheindex)aboveandtotheleft.Otherrootsaredefinedsimilarlyandidentifiedbytheindexgiven.(Insquareroot,anindexoftwoisunderstoodandusuallynotwritten.)Followingisalistofthefirstelevenperfect(...
To find the cube root of a number, you want to find some number that when multiplied by itself twice gives you the original number. In other words, to find the cube root of 8, you want to find the number that when multiplied by itself twice gives you 8. The cube root of 8, then, is 2, because 2 × 2 × 2 = 8. Notice that the symbol for cube root is the radical sign with a small three (called the index) above and to the left . Other roots are defined similarly and identified by the index given. (In square root, an index of two is understood and usually not written.) Following is a list of the first eleven perfect (whole number) cube roots.
To find the square root of a number that is not a perfect square, it will be necessary to find an approximate answer by using the procedure given in Example
. Example 1Approximate .
Since 62 = 36 and 72 = 49, then is between and .
Therefore, is a value between 6 and 7. Since 42 is about halfway between 36 and 49, y...