The discussion revolves around methods for simplifying calculations involving roots, specifically focusing on the expression $$\frac{\frac{1}{2}}{1-\frac{\sqrt{2}}{2}}$$. Participants explore various techniques for manipulating fractions and rationalizing denominators.
Participants generally agree on the methods discussed for simplifying the expression, but there is no consensus on whether there are alternative methods beyond those mentioned.
Some steps in the calculations are not fully detailed, and there may be assumptions about prior knowledge of mathematical concepts such as rationalization and the difference of squares.
wishmaster said:Im just wondering what is the easiest way to deal with calculations where roots are involved?
For example how do you solve this one?
$$\frac{\frac{1}{2}}{1-\frac{\sqrt{2}}{2}}$$Thank you for replies!
Prove It said:A rule of thumb for fractions is to get a common denominator and to always attempt to rationalise denominators.
What have you tried so far?
wishmaster said:To multiply the fraction with 2.
MarkFL said:I assume you mean to multiply by:
$$1=\frac{2}{2}$$
This is a good first step. :D What did you get in doing so?
wishmaster said:Yes,Mark,i did it so as you said. Actualy i understand this,but i am wondering if there some other way to deal with this...
And i got:
$$\frac{1}{2-\sqrt{2}}$$
MarkFL said:Okay, now you want to rationalize the denominator. Think of the difference of squares formula...
wishmaster said:I multiply fraction with $$(2+\sqrt{2})$$
So i got:
$$\frac{2+\sqrt{2}}{2}$$
thank you!MarkFL said:Good! You could choose to leave it like that, or express it as:
$$1+\frac{\sqrt{2}}{2}$$