# 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