Dividing Radicals

[Pencil]

I get the concept of dividing radicals but this one is really challenging me. I keep getting 49 and I know that that's not the answer. Please tell me how to proceed. Thanks in advance.

Problem:

sqrt(7) sqrt(42) / sqrt(3)

My Approach:

sqrt(7) sqrt(42) / sqrt(3)

= sqrt(49) * sqrt(3)

= sqrt(3) * sqrt(3)

= 147/3

= 49

 

[Ishuda]

I get the concept of dividing radicals but this one is really challenging me. I keep getting 49 and I know that that's not the answer. Please tell me how to proceed. Thanks in advance.

Problem:

sqrt(7) sqrt(42) / sqrt(3)

My Approach:

sqrt(7) sqrt(42) / sqrt(3)

= sqrt(49) * sqrt(3) <========== No

= sqrt(3) * sqrt(3) <========== No - doesn't even follow from line above

= 147/3 <========= NO! Where did this come from?

= 49

At least the second line above [the first No] is close but where did you get these equations. You do know, for example, that
sqrt(a) sqrt(a) = sqrt(a * a) = a
don't you?
I think you need to review radicals and the rules for combining them.

 

[Pencil]

Mr/Mrs/Miss Pencil, sqrt(42) = sqrt(7) sqrt(6), so that should be:
= sqrt(7) sqrt(7) sqrt(6) / sqrt(3)

I gave you that as a RULE on your 1st post; forgot already?
Did you not get it tattooed on your wrist as I suggested?

Another RULE: sqrt(n) sqrt(n) = n

So above becomes:
7 sqrt(6) / sqrt(3)

Continue...hint: concentrate on sqrt(6)

Wow, thanks. After your assistance I was able to see how repetitive these problems can be. It literally took one full page of computation just to finally arrive at 7 sqrt(2)! Now I have a good understanding of simplifying radical problems, but i just gotta keep practicing because clearly I continue to make stupid mistakes. Anyway, here was my approach at simplifying it.


Oh, and it's Mr Pencil

Solved problem:

7 sqrt(6) / sqrt(3)

= 7 sqrt(2) sqrt(3) / sqrt(3)

= 7 sqrt(2) sqrt(3) / sqrt(3) * sqrt(3) / sqrt(3)

= 7 sqrt(6) sqrt(9) / 3

= 7 sqrt(2) sqrt(3) sqrt(3) / 3

= 7*3 sqrt(2) / 3 (cancellation occurs here)

= 7 sqrt(2)