Question

How do you evaluate `\frac{\sqrt{4}}{2\sqrt{3}}`?

Answer 1

See a solution process below:

Explanation:

First, take the square root of `4` and cancel common terms in the numerator and denominator:

`sqrt(4)/(2sqrt(3)) => 2/(2sqrt(3)) => color(red)(cancel(color(black)(2)))/(color(red)(cancel(color(black)(2)))sqrt(3)) => 1/sqrt(3)`

To rationalize the denominator we multiply by the appropriate form of `1`:

`sqrt(3)/sqrt(3) xx 1/sqrt(3) => sqrt(3)/(sqrt(3))^2 => sqrt(3)/3`

If you need a specific number:

`sqrt(3)/3 => 1.732050/3 => 0.577` rounded to the nearest thousandth.