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multiplication of sqroots
- Thread starter angushiro
- Start date
Please show your work - If we don't see it, we don't know where you are stuck. And in this case, where we have to guess the order of operations, seeing your work might clue us in.I need help in how to multiply or simplify this problem> sqrt of 3-1 * the sqrt of 3+1
Is the question to simplify this expression?
\(\displaystyle (\sqrt{3} - 1) × (\sqrt{3} + 1)\)
Do you remember a rule for the product of sum and difference of the same two numbers?
If you don't remember that rule, use FOIL
Rationalizing The Denominator
Thank you for your answer. Where I am stuck is how to do this question: I do not have a sqrt symbol on my laptop so I must hopefully manage to show the question with characters. The question is this: Rationalize the Denominator of: 5*sqrt(3-2)/sqrt(3-1) I know I must conjugate the equation with multiplying the numerator and dominator with the opposite of: sqrt(3-1) then go on to simplify. But I am really stuck on how to do the operation with the 2 radicals with in the sqrt, I know the multiplication of the denominator is the difference between the square of (3-1)(3+1) but if someone could possibly give me an eg. I would understand better?? Thank you very much Angushiro
Thank you for your answer. Where I am stuck is how to do this question: I do not have a sqrt symbol on my laptop so I must hopefully manage to show the question with characters. The question is this: Rationalize the Denominator of: 5*sqrt(3-2)/sqrt(3-1) I know I must conjugate the equation with multiplying the numerator and dominator with the opposite of: sqrt(3-1) then go on to simplify. But I am really stuck on how to do the operation with the 2 radicals with in the sqrt, I know the multiplication of the denominator is the difference between the square of (3-1)(3+1) but if someone could possibly give me an eg. I would understand better?? Thank you very much Angushiro
You are way overcomplicating this.Thank you for your answer. Where I am stuck is how to do this question: I do not have a sqrt symbol on my laptop so I must hopefully manage to show the question with characters. The question is this: Rationalize the Denominator of: 5*sqrt(3-2)/sqrt(3-1) I know I must conjugate the equation with multiplying the numerator and dominator with the opposite of: sqrt(3-1) then go on to simplify. But I am really stuck on how to do the operation with the 2 radicals with in the sqrt, I know the multiplication of the denominator is the difference between the square of (3-1)(3+1) but if someone could possibly give me an eg. I would understand better?? Thank you very much Angushiro
\(\displaystyle \dfrac{5\sqrt{3 - 2}}{\sqrt{3 - 1}} = \dfrac{5\sqrt{1}}{\sqrt{2}} = \dfrac{5 * 1}{\sqrt{2}} = \dfrac{5}{\sqrt{2}} * \dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{5\sqrt{2}}{2}.\)
Either overcomplicating OR typing parentheses in the wrong place. To type square roots, type in function notation: sqrt(3). Also use parentheses to make the order of operations clear.You are way overcomplicating this.
\(\displaystyle \dfrac{5\sqrt{3 - 2}}{\sqrt{3 - 1}} = \dfrac{5\sqrt{1}}{\sqrt{2}} = \dfrac{5 * 1}{\sqrt{2}} = \dfrac{5}{\sqrt{2}} * \dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{5\sqrt{2}}{2}.\)
Did you intend that to mean5*sqrt(3-2)/sqrt(3-1)
5 * [sqrt(3) - 2] / [sqrt(3) - 1] ?
In rhat case, to rationalize the denominator, multiply the expression by
[sqrt(3) + 1] / [sqrt(3) + 1]
For the denominator, use the rule that gives square of the first minus square of the second. Do you know what [sqrt(3)]^2 is?
For the numerator, use FOIL to multiply binomials. If you need more help doing that, show us your work so we can see what is giving you trouble.
You're welcome, but it is such a simple problem that I do wonder whether you copied it correctly. Make sure the problem is what you think it is. Of course, sometimes the book or site makes an error when giving an answer. Why even I sometimes err (not as often as denis of course).Thank You JeffM the equation you put down is correct, but my course from Coursera mark the answer wrong. I will go back to the basics within Coursera and try the video again. Thanks very much >>
Because the problem they MEANT to give was close to what DrPhil guessed, namely:Thanks Jeffm I went back to Coursera and after querying forums someone said that they got it correct after submission apparently the answer is 13+3*sqrt(3)/2 How did they get 13??
\(\displaystyle Simplify\ \dfrac{5\sqrt{3} - 2}{\sqrt{3} - 1}.\)
\(\displaystyle \dfrac{5\sqrt{3} - 2}{\sqrt{3} - 1} = \dfrac{5\sqrt{3} - 2}{\sqrt{3} - 1} * \dfrac{\sqrt{3} + 1}{\sqrt{3} + 1} = \dfrac{5\left(\sqrt{3}\right)^2 + 5\sqrt{3}- 2\sqrt{3} - 2}{\left(\sqrt{3}\right)^2 - 1^2} = \dfrac{5 * 3 + 3\sqrt{3} - 2 }{3 - 1} = \dfrac{13 + 3\sqrt{3}}{2}.\)