Simplifying A Radical Expression | Algebra

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[damirdukic]

8:31 -- Note that at this point you could have avoided later negative signs by just using "2*sqrt(6) - 7", instead of "7 - 2*sqrt(6)" as you did here.

[andy_in_colorado]

I absolutely LOVE your OCD tendencies. I have a few of those myself including your views on logarithms (ln vs. log etc) and on and on.

[emersonchaves]

I just did long division of the denominator by the numerator, as it seems bigger, and actually found a solution. That was quick

[RobG]

I so enjoyed the 1st method, and had thought of conjugates at the start, in large part because of my steady viewing of your videos here.

[popitripodi]

I used the second one!!! I like it very much! The first was a little bit painful indeed ❤❤❤❤

[nidhisingh]

How did you assume that in 1st method, the answer's gonna be like the term of a√6+b√3....etc.?

[DrQuatsch]

I just wanted to get rid of the sqrt(6) in the denominator first, so I thought it might be a good idea to multiply the denominator by (1 - sqrt(2)), so that the sqrt(6) * 1 and the sqrt(3) * -sqrt(2) terms would cancel. Yes, it would give me a -sqrt(12) term, but that is just equal to -2sqrt(3). So it seemed worth it to reduce the amount of square roots in the denominator and maybe it would just give me a multiple of the numerator. Turns out it was exactly -1 * numerator if I did this, so obviously I needed to multiply the denominator by sqrt(2) - 1 instead to get the numerator.
I first did try the 2nd method, but only on the denominator to see if I could simplify it that way. Seemed a bit long, so I went to look for alternatives, mostly to reduce the amount of multiplications I needed to do to the numerator. And that's when I thought of multiplying by (1 - sqrt(2)), which is a term less than I had to use before. And I fully expected it to not work... but it did.

[scottleung]

Nice - I tried using the second method, but didn't know I only had to change the second sign in the denominator.

[bobbyheffley]

Are you doing this on an iPad? Notability can be used on an iPad.

[LevelUpLegend]

in the second method you made a mistake in cancelation