color(blue)("Assumption: "sqrt(50x^3)" is correct")Assumption: √50x3 is correct
Note that 32= 2^2xx2^2xx232=22×22×2
" " 50=5^2xx2 50=52×2
" "18=2xx9 = 2xx3^2 18=2×9=2×32
Given:" "sqrt(32x^2)+sqrt(50x^3)-sqrt(18x^2) √32x2+√50x3−√18x2
Write as:
""4xsqrt(2)+5xsqrt(2x)-3xsqrt(2)4x√2+5x√2x−3x√2
""4xsqrt(2)+5xsqrt(2)sqrt(x)-3xsqrt(2)4x√2+5x√2√x−3x√2
Factor out xsqrt(2)x√2
color(blue)(" "xsqrt(2)(4+5sqrtx-3) ) x√2(4+5√x−3)
color(blue)(" "xsqrt(2) (1+5sqrtx) ) x√2(1+5√x)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Suppose: "sqrt(50x^3)" should be "sqrt(50x^2))Suppose: √50x3 should be √50x2
Proposed:" "sqrt(32x^2)+sqrt(50x^2)-sqrt(18x^2) √32x2+√50x2−√18x2
Write as:
""4xsqrt(2)+5xsqrt(2)-3xsqrt(2)4x√2+5x√2−3x√2
color(blue)(=>6xsqrt(2))⇒6x√2