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# Simplifying square-root expressions: no variables (advanced)

Sal simplifies elaborate expressions with square roots. For example, he simplifies (4√20-3√45)/√35 as -√(1/7).

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• Did Sal make an error at , where there was a negative sign before the -sqrt5/sqrt35, but at he says the simplified version is simply a positive sqrt1/sqrt7?
• Yes he did! Good eye. He forgot to bring the negative over when we was simplifying! Oops! There should be a little bubble that pops up in the bottom corner that shows the correction though.
The correct answer should be -√(1/7)
• in the first example, at you have simplified it to -sqrt5/sqrt35, the proceed to rewrite this as -sqrt(5/35) and end with the result of -sqrt(1/7).

When solving this on my own, after i reached the step you were at at , I simplified it to:
-sqrt5 / (sqrt7)(sqrt5) and cancelled the sqrt5 to end with -1/sqrt(7).

I believe these are both correct, as your example of the whole fraction under the radical could simplify to my form, however which would be considered the most simple answer?
• They are both equivalent. It depends on how your instructor wants the answer to be really. Both are simple enough. Later on you'll learn to rationalize the denominator, so you'll most likely require to do that. You simply multiply - 1/√(7) by √(7) / √(7) which will give -√(7)/7.

P.S. He mas an error, forgetting to include his negative sign.
• Does anybody else find they can solve these and other problems but don't feel like they are fully understanding them?
• I think it's easy with maths to end up doing the manipulations, without really getting why the manipulations work. It's not satisfying that way (at least I find), as it feels like just going through the motions.

Something that helped me is when I realised that so much of the manipulations Sal is doing here are because of the the distributive property
I have found that by thinking about that property and it's implications, and really understanding it, a lot of other stuff then fell into place.
• So, did Mr. Khan drop the negative sign when he simplified from -sqrt(5/35) to sqrt(1/7)?
• Yes, he dropped the minus sign. And, there was a correction box that pops up at about in the video that said the answer should be - sqrt(1/7)
• Wait at , the answer is actually -sqrt1/-sqrt7?
• The problem with that is a negative divided by a negative is a positive, so by doing this, you will improperly eliminate the negative sign
(1 vote)
• when are you supposed to square root, simply divide, or simply multiply? I cant figure this out and keep getting my answers wrong. Iv'e been stuck on the practice problems for 2 hours now!
• When this happens to me, I use the hints in each problem. Walkthru the hints one by one. Compare what was done in the hint with what you did. If you did something different, chances are you have found your mistake. Try to learn the technique shown in the hint. Rework the problem from that point forward on your own. See if you can get it correct. If it is still wrong, go back to the hints. Step thru again. You may go thru more hints this time but will likely find another step that you didn't handle correctly. Use the hint as a tutorial to learn from your mistakes.
• isn't te awnser to the first question negative -sqrt(1/7) not sqrt(1/7)? at -
• Yes, you are correct. Good catch. Looks like Sal dropped the minus sign.
• Can any Genius? anyone rationalize this for me 1/√7 + 1/√2??
(1 vote)
• Do each fraction individually.
1/√7 (√7/√7) = √7/7
1/√2 (√2/√2) = √2/2
So, your expression is now: √7/7 + √2/2
To add, convert to LCD of 14
√7/7 (2/2) + √2/2 (7/7) = 2√7/14 + 7√2/14 = (2√7+7√2)/14

Hope this helps.