Question

Rationalise the denominator of the following:

`sqrt(3)/sqrt(7)`

Answer 1

Given: `sqrt(3)/sqrt(7)`

Step-wise calculation:

1. Multiply numerator and denominator by `sqrt(7)` to rationalise the denominator:

`sqrt(3)/sqrt(7) xx sqrt(7)/(sqrt(7)`

= `(sqrt(3) xx sqrt(7))/(sqrt(7) xx sqrt(7))`

2. Simplify the denominator: `sqrt(7) xx sqrt(7) = 7`

3. Simplify the numerator: `sqrt(3) xx sqrt(7) = sqrt(21)`

So the expression becomes `sqrt(21)/(7)`.

\[ \frac{\sqrt{3}}{\sqrt{7}} = \frac{\sqrt{21}}{7} \]

This is the rationalised form of the given expression.