How do you simplify #sqrt(24x)*sqrt(6x)#?

2 Answers
May 19, 2018

Answer:

#12x#

Explanation:

Given: #sqrt(24x)xxsqrt(6x)#

Note that 24 is the same as #4xx6 -> 2^2xx6#

So if we 'split up' the roots we have:

#color(white)("ddddddd")sqrt(2^2)xxsqrt(6)xx sqrt(x)xxsqrt(6)xxsqrt(x)#

Grouping the values:

#color(white)(dddddd"d") sqrt(2^2)xxubrace(sqrt(6)xxsqrt(6))xx ubrace(sqrt(x)xxsqrt(x))#

#color(white)(dddddd"ddd")ubrace(2color(white)("ddddd")xx6color(white)("dddddd")xx x)#

#color(white)(dddddd"ddddddddddd")12x#

May 19, 2018

Answer:

#12x#

Explanation:

#sqrt(24x)*sqrt(6x)#

#:.=sqrt(2*2*2*3x)*sqrt(6x)#

#sqrt2*sqrt2=2#

#:.=2sqrt(6x)*sqrt(6x)#

#:.=sqrt6x*sqrt6x=6x#

#:.=2*6x#

#:.=12x#