How do you simplify #\sqrt { 45x ^ { 5} } + \sqrt { 18x ^ { 6} } - \sqrt { 50x ^ { 6} } + \sqrt { 20x ^ { 5} }#?

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Answer 1 · 2018-03-13T16:57:49

See a solution process below:

We can simplify the radicals as:

#sqrt(9x^4 * 5x) + sqrt(9x^6 * 2) - sqrt(25x^6 * 2) + sqrt(4x^4 * 5x) =>#

#sqrt(9x^4)sqrt(5x) + sqrt(9x^6)sqrt(2) - sqrt(25x^6)sqrt(2) + sqrt(4x^4)sqrt(5x) =>#

#3x^2sqrt(5x) + 3x^3sqrt(2) - 5x^3sqrt(2) + 2x^2sqrt(5x)#

Next Group and Combine like terms:

#3x^2sqrt(5x) + 2x^2sqrt(5x) + 3x^3sqrt(2) - 5x^3sqrt(2) =>#

#(3 + 2)x^2sqrt(5x) + (3 - 5)x^3sqrt(2) =>#

#5x^2sqrt(5x) + (-2)x^3sqrt(2) =>#

#5x^2sqrt(5x) - 2x^3sqrt(2)#

Answer 2 · 2018-03-13T17:43:57

#5x^2sqrt5x-2x^3sqrt2#

#sqrt(45x^5)+sqrt(18x^6)-sqrt(50x^6)+sqrt(20x^5)#

#:.=sqrt(3*3*5*x*x*x*x*x)+sqrt(3*3*2*x*x*x*x*x*x)-sqrt(5*5*2*x*x*x*x*x*x)+sqrt(2*2*5*x*x*x*x*x)#

#:.sqrt 2 xx sqrt 2=2#
#:.sqrt 3 xx sqrt 3=3#
#:.sqrt 5 xx sqrt 5=5#
#:.sqrt x xx sqrtx=x#

#:.=3*x^2sqrt(5x)+3*x^3sqrt2-5x^3sqrt2+2x^2sqrt(5x)#

#:.=-2x^3sqrt2+5x^2sqrt(5x)#

#:.=5x^2sqrt(5x)-2x^3sqrt2#