Question

What is `4/(1+ sqrt3)`?

Answer 1

1.46410161514

Explanation:

Type into a calculator the following

4/ (1+√3)

So you do the denominator first and then the numerator.
If you don't want to use a calculator, then you can find the square root of 3 and then add that to 1.
After that, divide 4 by the sum of that.

Answer 2

`4/(1+sqrt(3)) = 2sqrt(3)-2`

Explanation:

While this could be evaluated directly using a calculator, I believe the intent was to simplify by rationalizing the denominator.

`4/(1+sqrt(3))`
`color(white)("XXX")=4/(1+sqrt(3))xx(1-sqrt(3))/(1-sqrt(3))`

`color(white)("XXX")=(4-4sqrt(3))/(1-(sqrt(3))^2)`

`color(white)("XXX")=(4-4sqrt(3))/(1-3)`

`color(white)("XXX")=(4-4sqrt(3))/(-2)`

`color(white)("XXX")=2sqrt(3)-2`