Express 7√(6)*5√(3) in the simplest radical form. Help

Okay, this is what I have so far:

7√6*5√3
=(7*5)(√6*√3)
=35*√18
=35*√9*2
-Here is where it starts to get odd-
=35*9√2
=315√2
At first I was wondering if the answer should be 315√2 or 630, so I checked it on an algebra online calculator, but it says the answer is 105√2

So now I'm completely confused. Please explain if I have the correct answer or not. If I do should it be expressed as 315√2 or 630. And if I don't, please explain in detail where I messed up and how they got the answer. Oh and I learn better with words than with numbers. Thank you all soooo much!

The answer is actually 105√2. You simplified √9 incorrectly. It's supposed to be 3, so 35*3√2 = 105√2.

I hope this helps!

Just like you did it..........

7√(6)*5√(3) = 35√18 = 105√2

When you took the 9 out of the 18 you forgot that it was √9 = 3 which is why 315 is incorrect

well
35*√9*2
=35*3*√2 (√9=3 this was your mistake)
=105*√2

7 sq rt 6 * 5 sq rt 3= 35 sq rt 18 35 sq rt 9 * sq rt 2= 105 sq rt 2