The discussion focuses on simplifying the expression 1/cuberoot(2). Participants explain that to rationalize the denominator, one can multiply by cuberoot(2) squared over itself, resulting in the expression (cuberoot(4)/2). The conversation also touches on the definition of "simplified," with some arguing that 1/cuberoot(2) is already a simple form, while others emphasize the importance of expressing fractions without radicals in the denominator. The use of LaTeX for mathematical expressions is encouraged for clarity.
PREREQUISITESStudents learning algebra, mathematics educators, and anyone interested in understanding the simplification of radical expressions.
What do you need to multiply ##\displaystyle \root 3 \of {2}## by to get ##2## ?barryj said:
Hi Barry,barryj said:
Well, you appear to know the trick already!barryj said:
Ideally we should say 'rationalise the denominator' (i.e. express with no surds in the denominator).gmax137 said:
That's what I think, but some mathematicians disagree:gmax137 said:
gmax137 said:
As well as virtually all high school algebra and college precalculus textbooks. As I said in the other thread that @PeroK linked to, the concept of "simplifying" fractions with radicals in the denominator means rewriting the fractions so that any radical now appears in the numerator. No doubt this topic precedes computers and calculators, but I'm sure that its basis is historical. For example, using a table to look up an approximation to ##\sqrt 2##, it's much quicker to calculate ##\frac{\sqrt 2}2 \approx \frac{1.4142}2## than it is to calculate ##\frac 1 {\sqrt 2} \approx \frac 1 {1.4142}##.PeroK said:
Yeah, mine does, too, but if you want more than 2 or so significant digits of precision, you'd do better by looking up ##\sqrt 2## in a table and then either dividing it by 2 or dividing it into 1.gmax137 said:
Mark44 said:
