How do I divide #sqrt(300x^18)/sqrt(2x)#?

1 Answer
Mar 6, 2017

Answer:

#5 sqrt(6x^17) = 5sqrt(6)x^(17/2)# assuming #x# is positive,

otherwise #(5 sqrt(6)sqrt(x^18))/sqrt(x)#

Explanation:

Use the square root property: #(sqrt(m))/(sqrt(n)) = sqrt(m/n)#

#(sqrt(300 x^18))/(sqrt(2x)) = sqrt((300 x^18)/(2x)) = sqrt((150x^18)/x)#

Use the exponent rules: #x^m/x^n = x^(m-n)# and #x^mx^n = x^(m+n)#

#sqrt((150x^18)/x)= sqrt(150x^17) #

Use the square root property: #sqrt(m*n) = sqrt(m) sqrt(n)#

#= sqrt(25 * 6 x^17) = sqrt(25)sqrt(6) sqrt(x^17) #

#= 5 sqrt(6x^17)#

Remember that #sqrt(m) = m^(1/2)#

So # 5 sqrt(6x^17) = 5sqrt(6)x^(17/2)#