## anonymous 5 years ago How would you fine the square root of this number: 3square root of 28?

1. anonymous

Is this 3*Sqrt(28)?

2. anonymous

I think so I'm doing a worksheet and I'm trying to workout the problem the answer is suppoed to 6 square root of 7

3. anonymous

3sqrt(28)=3sqrt(4*7)=3sqrt((2^2)*7)=3sqrt(2^2)sqrt(7)=3*2*sqrt7=6sqrt7

4. anonymous

How would you do the square root of this problem: -3 square root of 54. The answer is supposed to be -9 square root of 6.

5. anonymous

can you write 54 into product of prime numbers (1,2,3,5,7,11,....) for me?

6. anonymous

2,3,3,3

7. anonymous

my computer went crazy sorry for so many entries

8. anonymous

ok, there you have 54=2x3x3x3. there is a rule like this: sqrt(a^2)=a, a>0 so you have 54=2x3x3^2 sqrt54=sqrt(2x3x3^2)=sqrt(2x3) x sqrt(3^2) you do the rest for me? the thing here is you need to understand how it work, then you can do any problem

9. anonymous

I don't understand what you want me to do?

10. anonymous

-.- $-3\sqrt{54}=-3\sqrt{2*3*3^{2}}=-3\sqrt{6}\sqrt{3^{2}}=-3*3*\sqrt{6}=-9\sqrt{6}$

11. anonymous

but you still have to understand the method

12. anonymous

I understand how you factored it down but how do you get the answer of -9 square root of 6?

13. anonymous

√(3^2)=3, you understand this right? so√(54)=√(2*3*3^3)=√(6*3^3)=(√6)*(√3^3)=(√6)*3 then -3*√(54)=-3*(√6)*3=-3*3*(√6)=-9√6 clear?