Project #18870 - College Math

Everyone is familiar with the square root sign,√ .  It indicates we're supposed to "undo" the process of squaring a number.  Here's the simplest possible example. 22 = 2*2 = 4; √4=2.   In general, power expressions represent the process of raising some quantity to some power;  the corresponding radical indicates the number that was raised to that  power, producing the known quantity.

In general, there are two square roots for every number.  Returning to the example above;  22=4, but (-2)2 is also equal to 4. (Remember, a negative quantity times a negative quantity equals a positive quantity.)  So strictly speaking, √4=±2 .  This is read, "The square root of four is equal to plus or minus two," meaning "...is equal to either a positive two or a negative two."

We'll use both the positive and the negative root of a radical when we discuss the quadratic formula.  For the purposes of this assignment, however, we'll only be concerned with the principle value -- that is, the positive value -- of the square root.  (Remember that as you work the Case and SLP!)

Many useful formulas and mathematical expressions involve radicals.  For example, the formula for calculating the radius of a sphere, given the volume, requires calculation of a cube root.  In physics, calculating the absolute temperature of a body, given the heat energy it's radiating, requires taking a fourth root (the Stefan-Boltzman law. Google it.)  In economics, calculating the  amount of money that must be left on deposit for n years, to obtain a given yield, requires calculation of the nth root (Google "Compound Interest Formulas").  We could offer many more examples, but the message is clear.  Radical expressions are important.

For an introduction to radicals, see Mishra (2012).  For a succinct collection of rules for manipulating radical expressions, see Simmons (2012). 

An important technique for dealing with radicals is calculating the conjugate.  See Hornsby et al., 2012. 

For specific tricks and techniques for dealing with radical expressions, see Spector (2012a and b).  For a collection of lessons with worked-out solutions, see Coolmath.com (2012).

Subject Mathematics
Due By (Pacific Time) 12/08/2013 10:00 am
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