Question

I am very confused on how to rationalize a denominator, it just gets harder and harder.*will be using the V symbol again as a square root symbol.* I get how to rationalize something simple as V2/V7, I would get V14/7 as the answer, but I get confused on how to solve 1/V6 +2, this is the way I did it, and I know it's wrong.

1/V6 + 2 * V6 - 2/V6 - 2
1V6-2/V36 - 4
1V6 - 2/6-4
1V6 - 2/2

I don't get how to solve from here, would the 2's cancel out? and I'm left with 1V6.

And this is an even harder one...
V30 + 3V3/V30 - 3V3

Answer 1

(a+b)(a-b) = a² - b²

(√6 + 2)(√6 - 2) = (√6)² - 2² = 6-4 = 2

So, you end up with (√6 - 2)/2 = √6/2 - 1

Your lack of parentheses got you the wrong answer.

(√30 + 3√3)/((√30 - 3√3) * (√30 + 3√3)/(√30 + 3√3)

= (30 + 6√30 + 27) / (30-27)
= (57 + 6√30)/3 = 19 + 2√30