[SOLVED]Root calculations

wishmaster

Active member
Im just wondering what is the easiest way to deal with calculations where roots are involved?
For example how do you solve this one?

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

Thank you for replies!

Prove It

Well-known member
MHB Math Helper
Im just wondering what is the easiest way to deal with calculations where roots are involved?
For example how do you solve this one?

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

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?

wishmaster

Active member
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

Staff member
To multiply the fraction with 2.
I assume you mean to multiply by:

$$\displaystyle 1=\frac{2}{2}$$

This is a good first step. What did you get in doing so?

wishmaster

Active member
I assume you mean to multiply by:

$$\displaystyle 1=\frac{2}{2}$$

This is a good first step. 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:

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

MarkFL

Staff member
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:

$$\displaystyle \frac{1}{2-\sqrt{2}}$$
Okay, now you want to rationalize the denominator. Think of the difference of squares formula...

wishmaster

Active member
Okay, now you want to rationalize the denominator. Think of the difference of squares formula...
I multiply fraction with $$\displaystyle (2+\sqrt{2})$$

So i got:

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

MarkFL

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

So i got:

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

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

wishmaster

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

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

thank you!