MHB Help with how to do this equation

  • Thread starter Thread starter ajk426
  • Start date Start date
AI Thread Summary
To solve the equation \dfrac{8 - \sqrt{27}}{2 \sqrt{3}}, rationalizing the denominator involves multiplying by \dfrac{\sqrt{3}}{\sqrt{3}}. After this step, the result should be in the form a + b\sqrt{3}. There is confusion about the nature of the numbers a and b, as the problem's wording affects the uniqueness of the solution. If a and b are real numbers, there are infinitely many solutions, but if they are specified as rational numbers, the solution is unique. Clarification on the problem's requirements is essential for accurate resolution.
ajk426
Messages
2
Reaction score
0
Screenshot (60).png
 
Mathematics news on Phys.org
Hint: Rationalize the denominator: [math]\dfrac{8 - \sqrt{27}}{2 \sqrt{3}} = \dfrac{8 - \sqrt{27}}{2 \sqrt{3}} \cdot \dfrac{\sqrt{3}}{\sqrt{3}}[/math]

-Dan
 
I've done that but I'm not sure where to go from there.
 
ajk426 said:
I've done that but I'm not sure where to go from there.
You should have gotten a form that looks like [math]a + b \sqrt{3}[/math] so I don't know where the problem is. Please post what you got.

-Dan
 
When you multiplied both numerator and denominator by $\sqrt{3}$, what did you get?
 
Did the problem really say that a and b are real numbers? If so there are infinitely many correct answers. IF the problem had specified "rational number" then there would be a unique answer.
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

MHB Is this Trigonometric Expression a Constant Function of x?
Replies
2
Views
1K
MHB How to Convert Miles to Kilometers with a Conversion Chain
Replies
6
Views
1K
MHB Find the amount of sand in each bag
Replies
1
Views
1K
MHB Linear combination of sine and cosine function
Replies
3
Views
1K
MHB Can You Find the Angle in This Isosceles Triangle Problem?
Replies
1
Views
1K
MHB Prove the minimum is greater than or equal to 8
Replies
2
Views
2K
MHB Equation Logarithmic: Solve x | MHB Help
Replies
7
Views
3K
MHB 411.1.3.15 Prove A\cap(B/C)=(A\cap B)/(A\cap C)
Replies
2
Views
2K
MathHelpBoards.com merges with PF
Replies
42
Views
5K
MHB Can the Partial Sum of a Difficult Series be Solved with Induction?
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top