Question

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

Answer 1

`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))`