How do you simplify # sqrt( 32x^2) + sqrt( 50x^3) - sqrt( 18x^2)#?

1 Answer

Answer:

#color(blue)(" "xsqrt(2)(1+5sqrtx) )#. See explanantion

Explanation:

#color(blue)("Assumption: "sqrt(50x^3)" is correct")#

Note that #32= 2^2xx2^2xx2#
#" " 50=5^2xx2 #
#" "18=2xx9 = 2xx3^2#

Given:#" "sqrt(32x^2)+sqrt(50x^3)-sqrt(18x^2)#

Write as:

#""4xsqrt(2)+5xsqrt(2x)-3xsqrt(2)#

#""4xsqrt(2)+5xsqrt(2)sqrt(x)-3xsqrt(2)#

Factor out #xsqrt(2)#

#color(blue)(" "xsqrt(2)(4+5sqrtx-3) )#
#color(blue)(" "xsqrt(2) (1+5sqrtx) )#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Suppose: "sqrt(50x^3)" should be "sqrt(50x^2))#

Proposed:#" "sqrt(32x^2)+sqrt(50x^2)-sqrt(18x^2)#

Write as:

#""4xsqrt(2)+5xsqrt(2)-3xsqrt(2)#

#color(blue)(=>6xsqrt(2))#