Simplyfying radicals - Speech or Presentation Example

Mathematics: Simplifying Radicals al affiliations Simplifying radicals Radicals are same as roots. Roots of numbers are given by thesymbol √. The roots of numbers extend from the second or square root, third root fourth root and so on until the nth root. The nth root of a number say, m is given my n√ (m). In simplification of radicals, first we examine the number under the radical sign. If this number is in its simplest form and cannot be divided by any perfect square, then we conclude that the radical is in its simplest form and therefore cannot be reduced further.

However, if the number under the radical sign can be divided by a perfect square, then we do so. In dividing the number by a perfect square, we choose the largest possible perfect square that divides the number under the radical sign evenly. That is to say that, there will be no remainders, decimals or fractions.In simplifying the first expression, we proceed as follows.Remove the index notation and replace with the radical notation. Using the relationship between radicals and indices,n1/2 = √nTherefore,(54)1/2 = √ (54)Again from the product rule of indices,ma *mb = ma+bso,√ (54) = √ (52 *52)We then separate the two numbers, each under its own radical sign.

√ (52 *52) = √ (52) * √ (52)This simplifies to two principal roots5*5 =25For the second expression we simplify as follows.(m1/4 n1/2)2 (m2n3)1/2Again replacing the exponential notations with radical notations using the indices radical relation,The first bracket simplifies to {4√ (m)*√n} 2 Expanding the bracket,{4√m}2{√n }2This simplifies to n√mThe second bracket simplifies to√ (m2n3)Putting each term under its own radical sign √ (m2)*√ (n3)This simplifies tom*√ (n2n1)It further simplifies tom*n√nCombining the results of the first and second brackets{n√m}{m*n√n}Simplifying the expression yields m√(m)*n2√nCombining the two radicals,mn2√ (mn)ReferenceTussy, A. S., & Gustafson, R. D. (2006).

Elementary algebra (Custom ed.). Belmont, CA: Thomson Brooks/Cole.