Question

What is `2sqrt{32} + 3sqrt{50} - 3sqrt{18}`?

Answer 1

`14sqrt(2)`

Explanation:

`color(blue)(32=4^2*2 rarr sqrt(32)=4sqrt(2))`

`color(red)(50=5^2*2 rarr sqrt(50)=5sqrt(2))`

`color(green)(18=3^2*2 rarr sqrt(18)=3sqrt(2))`

Therefore
`color(white)("XXX")2color(blue)(sqrt(32))+3color(red)(sqrt(50))-3color(green)(sqrt(18))`

`color(white)("XXX")=2*color(blue)(4sqrt(2))+3*color(red)(5sqrt(2))-3*color(green)(3sqrt(2))`

`color(white)("XXX")=8sqrt(2)+15sqrt(2)-9sqrt(2)`

`color(white)("XXX")=14sqrt(2)`