Question

How do you simplify the expression 4 over square root of 7 + the square root of 3?

Answer 1

`(sqrt(7) - sqrt(3))`

Explanation:

`4/(sqrt(7)+sqrt(3))`
`color(white)("XXXXX")`rationalizing the denominator:
`=4/(sqrt(7)-sqrt(3))xx(sqrt(7)+sqrt(3))/(sqrt(7)+sqrt(3))`

`=(4(sqrt(7)+sqrt(3)))/((sqrt(7))^2-(sqrt(3))^2)`

`=(4(sqrt(7)+sqrt(3)))/(7-3)`

`=(cancel(4)(sqrt(7)+sqrt(3)))/cancel(4)`