The discussion revolves around simplifying the expression 1/cuberoot(2). Participants explore methods to manipulate the expression similarly to how 1/sqrt(2) can be simplified.
The conversation includes various perspectives on the definition of "simplified" and whether the expression 1/cuberoot(2) is already in a simple form. Some participants suggest that rationalizing the denominator is a common expectation, while others express that the original form may be sufficient.
There is an ongoing debate about the interpretation of simplification in mathematical expressions, particularly regarding the presence of radicals in the denominator. Some participants reference educational materials and historical context for these conventions.
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:
