Simplify the radical expression sqrt root 128w^2 Show all work and steps.

Answer 1

To simplify the radical expression sqrt(128w^2), we first need to break down 128 into its prime factors:

128 = 2*64
64 = 2*32
32 = 2*16
16 = 2*8
8 = 2*4
4 = 2*2

So, 128 can be written as 2^7.

Now we substitute 128 with 2^7 in the expression sqrt(128w^2):

sqrt(128w^2) = sqrt(2^7*w^2)

Using the property of radicals that sqrt(a*b) = sqrt(a)*sqrt(b), we can split the square root:

sqrt(2^7*w^2) = sqrt(2^7)*sqrt(w^2)

Now, simplify the square root of 2^7:

sqrt(2^7) = sqrt(128) = 2*sqrt(32) = 2*sqrt(2*16) = 2*sqrt(2*2*8) = 2*sqrt(2*2*2*4) = 2*2*2*sqrt(2) = 8*sqrt(2)

Now simplify the square root of w^2:

sqrt(w^2) = w

Combine the simplified square roots:

sqrt(128w^2) = 8w*sqrt(2)

Therefore, the simplified form of sqrt(128w^2) is 8w*sqrt(2).