# square roots

• September 19th 2008, 08:42 AM
fabxx
square roots
Page 473 #7
If $18\sqrt{18}$= $r\sqrt{t}$, where r and t are positive integers and r>t, which of the following could be the value of rt? I don't get why the answer is 108. Thanks in advance.
• September 19th 2008, 08:54 AM
Moo
Hello,
Quote:

Originally Posted by fabxx
Page 473 #7
If $18\sqrt{18}$= $r\sqrt{t}$, where r and t are positive integers and r>t, which of the following could be the value of rt? I don't get why the answer is 108. Thanks in advance.

$18=9 \times 2=2 \cdot 3^2$

Hence $\sqrt{18}=\sqrt{3^2 \cdot 2}=3 \sqrt{2}$

So $18 \sqrt{18}=\dots$

Can you finish it ?
• September 19th 2008, 09:11 AM
fabxx
I multiplied and I got 54 sqrt(2) which isn't correct since the correct answer from the book is 108. Why though?
• September 19th 2008, 09:15 AM
Moo
Quote:

Originally Posted by fabxx
I multiplied and I got 54 sqrt(2) which isn't correct since the correct answer from the book is 108. Why though?

$54 \sqrt{2}=r \sqrt{t}$
So $r=54$ and $t=2$

You're asked for rt, that is to say 54x2 (Wink)