I also need help simplifying these four radicals!
- Thread starter Hadramout
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D
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Dr.Peterson
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Apparently the last one is supposed to be (-2√5)^2. Be sure to use at least as many parentheses as you need; don't be sparing with them!
Do you know how to simplify a simple one, like √27? At least show us what you can do with that. Once you have that procedure right, try the others so we can see where you are hung up.
HallsofIvy
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It also helps to know that \(\displaystyle \sqrt{a}\sqrt{b}= \sqrt{ab}\) and \(\displaystyle \frac{\sqrt{a}}{\sqrt{b}}= \sqrt{\frac{a}{b}}\).
Yes, I know how to simplify the -2√5 squared. The second parenthesis was just to indicate that -2√5 was squared.
√27
/\
9 3
/ \
3 3
Therefore, it would be 3√3 times √9 which would equal 15.58845... and I don't think that the answer should end with a decimal, I'm just trying to make sure that I get this answer right. Unless 3√3 * √9 would be the final, simplified answer.
√27
/\
9 3
/ \
3 3
Therefore, it would be 3√3 times √9 which would equal 15.58845... and I don't think that the answer should end with a decimal, I'm just trying to make sure that I get this answer right. Unless 3√3 * √9 would be the final, simplified answer.
√27
/\
9 3
/ \
3 3
Therefore, it would be 3√3 times √9 which would equal 15.58845... and I don't think that the answer should end with a decimal, I'm just trying to make sure that I get this answer right. Unless 3√3 * √9 would be the final, simplified answer.
You were getting close on the first one.
[MATH]\sqrt{27} - \sqrt{9} = \sqrt{9 * 3} - \sqrt{9} = \left ( \sqrt{9} * \sqrt{3} \right ) - \sqrt{9}.[/MATH]
This is why we ask you to show your work. It is hard for us to help you if we cannot follow you thought process in detail. In any case, it was after here that you seem to go astray in your simplification. Obviously, you recognized that
[MATH]\sqrt{9} = 3.[/MATH]
So the next step should be
[MATH]\left ( \sqrt{9} \sqrt{3} \right ) - \sqrt{9} = 3\sqrt{3} - 3.[/MATH]
What next?
By the way, the square root of 3 is an irrational number so any number with a finite number of decimals is not an exact answer, merely an approximation. Unless you are asked for an answer to n decimals, do not convert radicals to decimal approximations unless it can be done exactly in rational form. Just leave irrational solutions in radical form.
[MATH]\sqrt{27} - \sqrt{9} = \sqrt{9 * 3} - \sqrt{9} = \left ( \sqrt{9} * \sqrt{3} \right ) - \sqrt{9}.[/MATH]
This is why we ask you to show your work. It is hard for us to help you if we cannot follow you thought process in detail. In any case, it was after here that you seem to go astray in your simplification. Obviously, you recognized that
[MATH]\sqrt{9} = 3.[/MATH]
So the next step should be
[MATH]\left ( \sqrt{9} \sqrt{3} \right ) - \sqrt{9} = 3\sqrt{3} - 3.[/MATH]
What next?
By the way, the square root of 3 is an irrational number so any number with a finite number of decimals is not an exact answer, merely an approximation. Unless you are asked for an answer to n decimals, do not convert radicals to decimal approximations unless it can be done exactly in rational form. Just leave irrational solutions in radical form.
pka
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You have the completely wrong idea as to what this site is all about.
We do not teach you how to work these questions.
You come here for help on what you do not understand.
What you may not understand cannot be the whole assignment.
If you simply want answers, then here: \(\displaystyle 1)~9\sqrt3,~~2)~3\sqrt5,~~3)~2\).
Those are from the back-of-the-book. They don't help you.
Dr.Peterson
Elite Member
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Please understand that what you wrote did not say that the -2√5 was squared. In order to express this in proper notation, you must put parentheses around the portion that is squared, as I showed: (-2√5)^2. The fact that we know what you meant doesn't mean that you have written what you meant, and that is part of what a math class is supposed to teach you.
As for the answer, when you are asked to "simplify", you do not give a decimal answer; you just leave it in the simplest radical form possible.
You have simplified √27 as 3√3; but that is only part of the expression. Your 3√3 * √9 is not as simple as you can get it. This is because, as has been pointed out, √a * √b = √(ab): you can combine a product of radicals into a single radical.
Usually, when you have such a product, the best procedure will be to combine first: √27 * √9 = √(27 * 9). Then simplify that. In this case, you can easily simplify √9; what number do you get? Then just simplify what's left.
(JeffM misread the problem, but apart from that his advice is good.)
As for how we operate, pka was a little abrupt, but correct: You can't expect us to teach material from scratch; for that, listen in class, read your book, watch videos, or whatever. We're here so you can get the personal interaction you need after that: Show us your work, so we can see what parts you need help with, and then we can talk it through. That is, you walk us through what you can do, and we help you from there. Are you willing to do that?
If you haven't, please read the submission guidelines you were referred to.
D
Deleted member 4993
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Are you taking a class where this set is a home-work?