Question

Rationalise the denominator of the following and hence find their value by using `sqrt(2) = 1.414` and `sqrt(3) = 1.732`:

`13/(4 + sqrt(3))`

Answer 1

Given: `13/(4 + sqrt(3))`

Step-wise calculation:

1. Multiply the numerator and denominator by the conjugate of the denominator `4 - sqrt(3)` to rationalise the denominator: 

`13/(4 + sqrt(3)) xx (4 - sqrt(3))/(4 - sqrt(3))`

= `(13(4 - sqrt(3)))/((4 + sqrt(3))(4 - sqrt(3))`

2. Use the difference of squares in the denominator:

`(4)^2 - (sqrt(3))^2`

= 16 – 3

= 13

3. Simplify:

`(13(4 - sqrt(3)))/13 = 4 - sqrt(3)`

4. Substitute `sqrt(3) = 1.732`: 

4 – 1.732 = 2.268