Question

Rationalise the denominator and simplify to find the value of `4/(sqrt(5) + sqrt(3))`, given that `sqrt(5) = 2.236` and `sqrt(3) = 1.732`

Answer 1

We are asked to simplify and evaluate:

`4/(sqrt(5) + sqrt(3))`, where `sqrt(5) = 2.236, sqrt(3) = 1.732`

Step 1: Rationalise the denominator

Multiply numerator and denominator by the conjugate `(sqrt(5) - sqrt(3))`:

`4/(sqrt(5) + sqrt(3)) xx (sqrt(5) - sqrt(3))/(sqrt(5) - sqrt(3))`

= `(4(sqrt(5) - sqrt(3)))/((sqrt(5))^2 - (sqrt(3))^2`

Step 2: Simplify denominator

`(sqrt(5))^2 - (sqrt(3))^2`

= 5 – 3

= 2

So, `(4(sqrt(5) - sqrt(3)))/2 = 2(sqrt(5) - sqrt(3))`

Step 3: Substitute values

`2(sqrt(5) - sqrt(3))`

= 2(2.236 – 1.732)

= 2(0.504)

= 1.008