Root Calculations: Easiest Way to Solve?

[theakdad]

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]

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!

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?

 

[theakdad]

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?

To multiply the fraction with 2.

 

[MarkFL]

To multiply the fraction with 2.

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?

 

[theakdad]

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?

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]

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:

$$\frac{1}{2-\sqrt{2}}$$

Okay, now you want to rationalize the denominator. Think of the difference of squares formula...

 

[theakdad]

Okay, now you want to rationalize the denominator. Think of the difference of squares formula...

I multiply fraction with $$(2+\sqrt{2})$$

So i got:

$$\frac{2+\sqrt{2}}{2}$$

 

[MarkFL]

I multiply fraction with $$(2+\sqrt{2})$$

So i got:

$$\frac{2+\sqrt{2}}{2}$$

Good! You could choose to leave it like that, or express it as:

$$1+\frac{\sqrt{2}}{2}$$

 

[theakdad]

Good! You could choose to leave it like that, or express it as:

$$1+\frac{\sqrt{2}}{2}$$

thank you!

 

[MarkFL]

I have created a new topic for your new question. We discourage the tagging on of new questions to an existing topic so that topics do not become a successive string of questions being discussed.

The new topic is here:

http://mathhelpboards.com/pre-algebra-algebra-2/isolating-radical-7480.html