MHB Root Calculations: Easiest Way to Solve?

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The discussion centers on finding the easiest method to solve calculations involving roots, specifically the expression $$\frac{\frac{1}{2}}{1-\frac{\sqrt{2}}{2}}$$. A common approach suggested is to obtain a common denominator and rationalize the denominator. Participants shared their steps, including multiplying by $$\frac{2}{2}$$ to simplify the expression to $$\frac{1}{2-\sqrt{2}}$$. Further, they discussed rationalizing the denominator using the difference of squares, leading to the final result of $$\frac{2+\sqrt{2}}{2}$$ or expressed as $$1+\frac{\sqrt{2}}{2}$$. The conversation emphasizes practical techniques for handling root calculations effectively.
theakdad
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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!
 
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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!

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?
 
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?

To multiply the fraction with 2.
 
wishmaster said:
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?
 
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?

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:

$$\frac{1}{2-\sqrt{2}}$$
 
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:

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

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

$$\frac{2+\sqrt{2}}{2}$$
 
wishmaster said:
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:

$$1+\frac{\sqrt{2}}{2}$$
 
MarkFL said:
Good! You could choose to leave it like that, or express it as:

$$1+\frac{\sqrt{2}}{2}$$
thank you!
 
  • #10
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
 

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