How do you simplify sqrt( 32x^2) + sqrt( 50x^3) - sqrt( 18x^2)32x2+50x318x2?

1 Answer

color(blue)(" "xsqrt(2)(1+5sqrtx) ) x2(1+5x). See explanantion

Explanation:

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+50x318x2

Write as:

""4xsqrt(2)+5xsqrt(2x)-3xsqrt(2)4x2+5x2x3x2

""4xsqrt(2)+5xsqrt(2)sqrt(x)-3xsqrt(2)4x2+5x2x3x2

Factor out xsqrt(2)x2

color(blue)(" "xsqrt(2)(4+5sqrtx-3) ) x2(4+5x3)
color(blue)(" "xsqrt(2) (1+5sqrtx) ) x2(1+5x)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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+50x218x2

Write as:

""4xsqrt(2)+5xsqrt(2)-3xsqrt(2)4x2+5x23x2

color(blue)(=>6xsqrt(2))6x2