Rationalise the denominator

We know:

Rationalise = turn into a fraction 

We know:

Denominator = the bottom part of the fraction 

So,

Put them together

Rationalise the denominator = Turn the bottom part of the fraction into a fraction.

NOTE: 

 A number divided by itself = 1

And has no effect on an equation.

Therefore  `x^2/x^2=1 or sqrt7/sqrt7=1`

 

Examples

1.  Rationalise the denominator

`10/sqrt7`

`10/{sqrt7timessqrt7/sqrt7}=10/{{sqrt7timessqrt7}/sqrt7}=10/{7/sqrt7}`

So we have now rationalised the denominator

i.e.

`10/sqrt7=10/(7/sqrt7)`

But we can go further:

`10/(7/sqrt7)={10timessqrt7}/7`

Answer:  `10/sqrt7={10sqrt7}/7` 

 

2.  Rationalise the denominator 

 `{A}/sqrtB`

`A/{sqrtBtimessqrtB/sqrtB}=A/{{sqrtBtimessqrtB}/sqrtB}=A/{{B}/sqrtB}`

So we have now rationalised the denominator

i.e.

`A/sqrtB=A/(B/sqrtB)`

But we can go further:

 `A/(B/sqrtB)={AtimessqrtB}/B`

Answer:  `A/sqrtB={AsqrtB}/B`

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