Question

How do you rationalize the denominator and simplify `[(x+3)^(1/2)-(x)^(1/2)] / 3`?

Answer 1

`((x+3)^(1/2)-(x)^(1/2))/3=1/((x+3)^(1/2)+(x)^(1/2))`

Explanation:

The denominator is a natural number and it appears as you wanted to rationalize numerator. This is done as follows:

`((x+3)^(1/2)-(x)^(1/2))/3`

= `((x+3)^(1/2)-(x)^(1/2))/3xx((x+3)^(1/2)+(x)^(1/2))/((x+3)^(1/2)+(x)^(1/2))`

= `((x+3)-(x))/(3((x+3)^(1/2)+(x)^(1/2)))`

= `3/(3((x+3)^(1/2)+(x)^(1/2)))`

= `1/((x+3)^(1/2)+(x)^(1/2))`