<p>If 18<em>sqrt(18) = r</em>sqrt(t), where r and t are positive integers and r > t, which of the following could be the value of r*t?</p>
<p>A: 18
B: 26
C: 108
D: 162
E: 324</p>
<p>Answer is C</p>
<p>Please help, I don't know how to solve it.</p>
<p>so you basically have this:
18 * (18)^(1/2) = r * (t)^(1/2).
so i would solve it like this:
set r as 18 (outside the root) and t as 18 (inside the root)
so factoring 18 gives 2 * 3^2.
You have to satisfy the requirement given, which is r>t.
therefore, you have to take the 3^2 out of the square root.
so you get this
(2 * 3^2) * (2 * 3^2)^(1/2)
(2 * 3^2) * 3 * (2)^(1/2) which is 2 * 3^2 * 3 * sqrt(2)
so you have
54 = r and t=2.
multiply and you get 108.</p>
<p>showing math is sort of confusing, so tell me if i need to clarify.</p>
<p>18sqrrt(18) = (18* 3)sqrrt(2)
Because sqrrt(18)=sqrrt(9*2)=3sqrrt(2)</p>
<p>R=18<em>3
T=2
rt=18</em>3*2=108</p>
<p>Thank you very much for the help! I understand it now :D</p>