How do you simplify #4sqrt(8x^8y^6z^5) times 4sqrt(2x^2y^2z) #?

Question

How do you simplify #4sqrt(8x^8y^6z^5) times 4sqrt(2x^2y^2z)  #?

Avery Alexander · Accepted Answer

#64x^5y^4z^3#

You can simplify each root as far as possible and then multiply the answers.

Or you can multiply the two roots together first and then find the square root of the product. I will follow the second option.

#4sqrt(8x^8y^6z^5) times 4sqrt(2x^2y^2z) #

#=4xx4sqrt(8x^8y^6z^5 times 2x^2y^2z) #

#= 16sqrt(16x^10y^8z^6)#

#= 16 xx4x^5y^4z^3" "larr# divide the indices by #2#

#= 64x^5y^4z^3#

Hazel Anglin · Answer

undefined To simplify the expression 4√(8x^8y^6z^5) times 4√(2x^2y^2z), we can multiply the coefficients and combine the square roots.

First, multiply the coefficients: 4 times 4 equals 16.

Next, simplify the square roots: 
√(8x^8y^6z^5) times √(2x^2y^2z) equals √(8x^8y^6z^5 * 2x^2y^2z).

To simplify the expression inside the square root, we can multiply the coefficients and combine the variables with the same base and exponent.

8 times 2 equals 16.
x^8 times x^2 equals x^(8+2) which is x^10.
y^6 times y^2 equals y^(6+2) which is y^8.
z^5 times z equals z^(5+1) which is z^6.

Therefore, the simplified expression is 16√(16x^10y^8z^6).