Question 600330
To rationalize the denominator, you simply multiply top and bottom of the fraction by the conjugate of the denominator. In general, the conjugate of {{{sqrt(x)}}} is {{{sqrt(x)}}} (the conjugate is itself)




{{{5/(sqrt(3))}}} Start with the given expression.



{{{(5*sqrt(3))/(sqrt(3)*sqrt(3))}}} Multiply top and bottom by {{{sqrt(3)}}}



{{{(5*sqrt(3))/(sqrt(3*3))}}} Combine the roots.



{{{(5*sqrt(3))/(sqrt(9))}}} Multiply



{{{(5*sqrt(3))/(3)}}} Take the square root of 9 to get 3.



So {{{5/(sqrt(3))}}} completely simplifies to {{{(5*sqrt(3))/(3)}}}



In other words, {{{5/(sqrt(3))=(5*sqrt(3))/(3)}}}