square root question?

Question

I am trying to simplify:

square root of 24a^3b^6c

can someone please show me the process? thanks

Answer 1

1) 24 is the product of 4*6 , we can take the square root of 4 which is 2,but we can't simplify the 6 any more
so square root of 24 is 2square root of 3.
2)a^3 = a^2 * a^1 ,so we can take the square root of a^2 which is = a
so square root of a^3 =a square root of a.
3) b^6 = b^2 * b^2 * b^2 , now we can take the square root of each b^2 , so the answer for this part will be b^3,but we have to put this b^3 inside an absolute value ( check the algebra II textbook ).
4) c will stay inside the square root.

so the final answer is : 2aIb^3I square root of 6ac.
or: 2a absolute value of b^3 times square root
of 6ac .

I hope this would help

Answer 2

24 a^3 b^6 c

You can take them one at a time:
sqrt(24) = sqrt(4)sqrt(6) = 2 sqrt(6)

Now for the letters, sqrt(x^n) = x^(n/2)
sqrt(a^3) = a^(3/2)
sqrt(b^6) = b^(6/2) = b^3
sqrt(c) = c^(1/2)

Putting it back together:
2 sqrt(6) a^(3/2) b^3 c^(1/2)

Alternatively, your book might say to turn:
sqrt(a^3) into sqrt(a^2 * a) = a sqrt(a)
And it may tell you to leave c alone. In that case the answer would be:
2 sqrt(6) a sqrt(a) b^3 sqrt(c)

Answer 3

2*sqrt(6) * a^(3/2) * b^3 * c^(1/2)