2 ай бұрын
3 ай бұрын
Пікірлер
@RealMesaMike Ай бұрын
Yes, only one answer.. Thanks for solving the quadratic the right way and npt just asserting that you can "take the square root of both sides."
@nbsivakumar Ай бұрын
Thank you Sir. You are right 👍
@rob876 Ай бұрын
by definition, √25 = 5
@archangecamilien1879 2 ай бұрын
One way to do it is simply realize that |a|=+-a, lol...go through each case, either a=-b, or a=b, etc, show that in each of those cases, that implies that a^2=b^2...
@yuminanirvalen 2 ай бұрын
Sqrt(25) is 5 if that's how we define the function f = sqrt(x) as we usually do. But there exists another function g that is also a root with the solution -5. It's that simple. For the x^2 there exist n roots, people just casually write sqrt and mean both sometimes, but you have to differentiate between the two functions and if you do that it becomes simple as it is straightforward.
@nbsivakumar 2 ай бұрын
Very well explained. Thank you.
@chrismcgowan3938 2 ай бұрын
Did you not just prove that your original statement ( sqrt(25) = 5 only ) is not true. I would have said +or-5 is correct. Have I missed the point here, did you not just prove yourself wrong?
@nbsivakumar 2 ай бұрын
Of course I solved an equation which has both +5 and -5 as the values of x. But what if I just ask you a question ' What is square root of 25?' and what would your answer be?
@yuminanirvalen 2 ай бұрын
@@nbsivakumar My answer would be: What square root function do you take? 😅. There are two of them. If you take one it gives 5, the other gives -5. It's that simple.
@RealMesaMike Ай бұрын
@@yuminanirvalen "The Square Root" of X is a non-negative number, by definition of the square root function.
@nbsivakumar Ай бұрын
@@yuminanirvalen I'm just talking about square root of a positive constant. If you consider the square root function, which cannot have a behavior below x-axis. So whichever positive value that you choose for x, the corresponding y value is just positive. So my explanation concludes that square root of a positive number is always positive which can never be negative.
@chrismcgowan3938 Ай бұрын
@@nbsivakumar I would say + 5 or -5 I was taught this way. If the question was "what is the positive root of SQR(25) : then 5 is the only answer.
@edsiljess2137 2 ай бұрын
very informative
@nbsivakumar 2 ай бұрын
Thank you teacher Edsil.
@Grecks75 2 ай бұрын
The term "root" can mean slightly different things in different contexts: 1) Given a polynomial equation, the term "root" can be understood as any one of the solutions of the equation as an algebraic (real or complex) number. For example, in the (quadratic) equation x^2 - 25 = 0, both -5 and 5 are usually called (square) roots of the polynomial equation of degree 2. 2) On the other hand, if you want to define an n-th root _function_ that shall serve as a right-inverse of the function y=f(x)=x^n (note that f is not injective!), you need to define which one of the n n-th roots of the equation x^n - y = 0 (in the complex plane) you want to have as your function's value. In Complex Analysis this is called the principal value of the n-th root function. For the real-valued square root function this is (always) the non-negative root. For the complex-valued square root function this is usually the one with the largest real part (and a positive imaginary part if there are two distinct roots with the same largest real part.) This way the square root function is usually made single-valued. So to sum it up for real numbers: The square root of a positive real number is always a positive real number, and the square root of zero is zero. The square root of a negative real number only exists as a complex number (in which case we usually chose the one in the upper half-plane, on the positive imaginary axis).
@nbsivakumar 2 ай бұрын
Very well Explained. Thank you.
@empsmiley5074 2 ай бұрын
Tr. Siva, Please keep uploading videos.👍👍 Nice explanation.
@nbsivakumar 2 ай бұрын
Sure Rachel. Thank you 👍👍
@Prachi-e2i 2 ай бұрын
Excellent tr siva. 🎉😊
@nbsivakumar 2 ай бұрын
Thank you Prachi 😊
@empsmiley5074 2 ай бұрын
👍👍👍
@nbsivakumar 2 ай бұрын
👍👍👍
@empsmiley5074 2 ай бұрын
👍👍👍
@nbsivakumar 2 ай бұрын
👍👍
@danielenascioli900 2 ай бұрын
The answer depends entirely on the type of numbers, for example if x belongs to the set of natural numbers then the answer is only +5, if instead we are in the set of real numbers then the answer can be |5| the absolute of 5 if there is just one x or +5 and - 5 if there are two x's.
@nbsivakumar 2 ай бұрын
So You agree with what I said?
@danielenascioli900 2 ай бұрын
@@nbsivakumar Yes, I just wanted to give a more complete answer.
@nbsivakumar 2 ай бұрын
@@danielenascioli900 Thank you for the explanation. Sharing knowledge is what we do at all times. Appreciated very much.
@bjornfeuerbacher5514 2 ай бұрын
"The answer depends entirely on the type of numbers" The answer to what? The answer to "what is the square root of 25", or the answer to "what are the solutions of x² = 25"? Do you realize that these two questions have different answers? "if instead we are in the set of real numbers then the answer can be |5| the absolute of 5" Which is just equal to 5, so there is no need at all to write |5|.
@danielenascioli900 2 ай бұрын
@@bjornfeuerbacher5514 To put it simply, there are Natural numbers(from 0 to + infinite) and Real numbers(from - infinite to + infinite), having said this, let's analyze the following cases: X=square root 25 with X=Natural number, in this case the answer is 5; X^2 = square root 25 with X=Natural number, the answer is only +5 because -5 is not a Natural number X^2 = square root 25 with X = Real number, answers are X1 = +5 and X2 = -5 X = square root 25 with X = Real number, as in the previous case the answers are both +5 and - 5, but the problem is that each X always corresponds to a numerical value, consequently the concept of absolute value was born which is a way of saying that this number is both positive how negative.
@empsmiley5074 2 ай бұрын
Well explained👍, Tr Siva.
@nbsivakumar 2 ай бұрын
Thank you Rachel.
@MinOo-h3l 2 ай бұрын
thank u for explaining sir!
@nbsivakumar 2 ай бұрын
You Welcome.
@Prachi-e2i 2 ай бұрын
Good good 👍 👌 👏
@nbsivakumar 2 ай бұрын
Thank you.
@TheHalonexus 2 ай бұрын
as far as I remember functions are defined as always having one output for all defined inputs, and for sqrt they just chose the positive half the same way arcsin arccos and such are defined on a very narrow range of outputs to guarantee 1 output for all inputs. So when solving equations you just have to keep in mind that -sqrt(x) is also a potential solution.
@nbsivakumar 2 ай бұрын
Your Definition on Functions is perfect. Thank you for the detailed explanation. Hope you agree.
@Prachi-e2i 2 ай бұрын
I understand mr siva😊😊
@nbsivakumar 2 ай бұрын
Thank you Prachi 😊😊❤
@CharlesHaruna-kb7rb 2 ай бұрын
Charles haruna 1123 Harlan street mare do Texas 79045
@Prachi-e2i 2 ай бұрын
I agree 👍
@nbsivakumar 2 ай бұрын
Thank you.
@star7mdy355 2 ай бұрын
Very good keep it up🎉🎉
@nbsivakumar 2 ай бұрын
Thank you.
@empsmiley5074 3 ай бұрын
The way you explain is interesting. Good, Tr.Siva👍.
@nbsivakumar 3 ай бұрын
Thank you Rachel👍
@empsmiley5074 3 ай бұрын
Nice explanation👍.
@nbsivakumar 3 ай бұрын
Thank you Rachel.
@empsmiley5074 3 ай бұрын
👍👍👍 Good.
@nbsivakumar 3 ай бұрын
Thank you Rachel.
@People_of_Ghats 3 ай бұрын
Wishes Shiva na..🎉
@nbsivakumar 3 ай бұрын
Thank you.
@N4TH3N96 3 ай бұрын
W video
@nbsivakumar 3 ай бұрын
Thank you.
@jcairtravels9935 3 ай бұрын
Great. Very useful
@nbsivakumar 3 ай бұрын
Thank you James.
@star7mdy355 3 ай бұрын
fantastic explainning.
@nbsivakumar 3 ай бұрын
Thank you.
@Prachi-e2i 3 ай бұрын
The video is educational.
@nbsivakumar 3 ай бұрын
Thank you Prachi.
@jagadeeshraman7120 3 ай бұрын
Well explained sir. Thank you.
@nbsivakumar 3 ай бұрын
Thank you Jagadeesh.
@ragulsathish 3 ай бұрын
Understood Clearly Sir
@nbsivakumar 3 ай бұрын
Thank you Ragul.
@empsmiley5074 3 ай бұрын
I look forward to learning new videos, Tr. Siva.
@nbsivakumar 3 ай бұрын
Sure Rachel. Please watch the video which I uploaded today and comment as well. Thank you.