"Rationalizing the denominator" is when we relocate a source (like a square source or cuberoot) native the bottom of a fraction to the top. |

## Oh No! an Irrational Denominator!

The bottom that a fraction is called the **denominator**. **Numbers choose 2 and also 3 are rational.But numerous roots, such as √2 and √3, are irrational.You are watching: How to move denominator to numerator**

### Example: has an Irrational Denominator

**To be in "simplest form" the denominator need to not** it is in irrational!

Fixing that (by making the denominator rational)**is referred to as "Rationalizing the Denominator**"

Note: there is nothing **wrong** with an irrational denominator, that still works. However it is not "simplest form" and so **can cost you marks**.

And removing lock may aid you settle an equation, so you should find out how.

So ... Exactly how do we perform it?

## 1. Multiply Both Top and Bottom through a Root

Sometimes we have the right to just multiply both top and also bottom by a root:

### Example: has an Irrational Denominator. Let"s fix it.

Multiply top and bottom by the square root of 2, because: √2 × √2 = 2:

Now the denominator has a rational number (=2). Done!

Note: the is yes sir to have actually an irrational number in the height (numerator) of a fraction.

## 2. Multiply Both Top and Bottom by the Conjugate

There is one more special method to relocate a square root from the bottom the a fraction to the peak ... We **multiply both top and also bottom **by the** conjugate of the denominator**.

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The conjugate is where we **change the authorize in the middle** of 2 terms:

x2 − 3 | x2 + 3 |

**another Example that is Conjugate**

a + b3 | a − b3 |

**It works since when we multiply something by the conjugate we acquire squares** favor this:

(a+b)(a−b) = a2 − b2

Here is exactly how to execute it:

How deserve to we move the square root of 2 come the top?

We have the right to multiply both top and bottom by 3+√2 (the conjugate of 3−√2), which won"t change the worth of the fraction:

*1***3−√2** × *3+√2***3+√2** = *3+√2***32−(√2)2** = *3+√2***7**

(Did you check out that we offered **(a+b)(a−b) = a2 − b2** in the denominator?)

Use her calculator to job-related out the worth before and after ... Is it the same?

There is one more example on the page assessing Limits (advanced topic) where I move a square root from the height to the bottom.

### Useful

So try to mental these little tricks, it may aid you solve an equation one day!