# [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!