Rationalize the denominator and simplify - help

[mcruz65]

?(81/40)
?81/?40=9/?40

In order to rationalize the denominator, I begin by factoring the denominator 40.
40 = 2 x 2 x 2 x 5

I am not getting anywhere with this line of logic. What am I doing wrong??

 

[wjm11]

?(81/40)
?81/?40=9/?40

In order to rationalize the denominator, I begin by factoring the denominator 40.
40 = 2 x 2 x 2 x 5

I am not getting anywhere with this line of logic. What am I doing wrong??

You don't need to factor the 40. We'd do that if we wanted to simplify it, which you might want to do before stating the final answer.

To "rationalize the denominator," multiply both the top and bottom (numerator and denominator) by the radical in the denominator. The denominator then becomes

(40^.5)(40^.5) = 40

 

[mcruz65]

If I multiply the numerator and the denominator by the denominator I get the following
?(81/40)?40/40=3240/1600=2.025

(40^.5)(40^.5) = 40 I don't understand how you arrive at this?? Please explain.

 

[wjm11]

(40^.5) equals the square root of 40.

You had 9/(40^.5)

If you multiply top and bottom by (40^.5), you have

[9(40^.5)]/[(40^.5)(40^.5)] = [9(40^.5)]/40

(40^.5) can be simplified to 2(10^.5). Use that to simplify your final answer.