Question

Determine whether sqrt(a)+sqrt(a)=2a is sometimes, always, or never true

Answer 1

Answer: Sometimes (don't ridicule if wrong hehe :) 

Answer 2

This is sometimes true; it is only true for a=1 or a=0.

We can combine radicals much as we do variables:

`√(a)+√(a)=2a \\ \\2√(a)=2a`

Divide both sides by 2:

`(2√(a))/(2)=(2a)/(2) \\ \\√(a)=a`

We can cancel the square root by squaring both sides:

`(√(a))^2=a^2 \\ \\a=a^2`

Now we can divide by a:

`(a)/(a)=(a^2)/(a) \\ \\1=a`

However, if we use a=0 this also works.