Question

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

`7/(3 - sqrt(2))`

Answer 1

Given: `7/(3 - sqrt(2))`

Step-wise calculation:

1. Multiply numerator and denominator by the conjugate of the denominator to rationalise:

`7/(3 - sqrt(2)) xx (3 + sqrt(2))/(3 + sqrt(2))`

= `(7(3 + sqrt(2)))/((3)^2 - (sqrt(2))^2`

2. Simplify the denominator:

9 – 2 = 7

3. So the expression becomes:

`(7(3 + sqrt(2)))/7 = 3 + sqrt(2)`

4. Using `sqrt(2) = 1.414`,

3 + 1.414 = 4.414