MHB Rationalize expression (5+2√6)/(7+4√3)

  • Thread starter Thread starter parry
  • Start date Start date
  • Tags Tags
    Expression
Click For Summary
To rationalize the expression (5+2√6)/(7+4√3), the first step is to multiply both the numerator and denominator by the conjugate of the denominator, which is (7-4√3). This process eliminates the square root in the denominator, making it easier to express the fraction in the form a-b√3. After performing the multiplication and simplifying, the values of a and b can be determined. The discussion emphasizes the importance of starting with the rationalization technique to solve the problem effectively.
parry
Messages
1
Reaction score
0
5+2 root 6 / 7+4root3 = a-b root3 find a and b
 
Mathematics news on Phys.org
Hello and welcome to MHB! (Wave)

I've moved this thread to our elementary algebra forum, since this is a better fit for the problem and I've give the thread a descriptive title. We are given:

$$\frac{5+2\sqrt{6}}{7+4\sqrt{3}}=a-b\sqrt{3}$$

And instructed to find $a$ and $b$. Do you have any work to show or thoughts on how to begin?
 
Start by "rationalizing the denominator". That is, multiply both numerator and denominator of [math]\frac{5+ 2\sqrt{6}}{7+ 4\sqrt{3}}[/math] by [math]7- 4\sqrt{3}[/math].
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Exploring Unconventional Addition: Can Mathematics Embrace New Foundations?
  • · Replies 8 ·
Replies
8
Views
2K
MHB What is the area of a triangle given (2, 3), (4, 5), and (6, 7)?
  • · Replies 6 ·
Replies
6
Views
2K
MHB Divisibility of (1!+2!+3!+...+100!)^2 by 5
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Geometry problem of interest with a 3-4-5 triangle
  • · Replies 59 ·
2
Replies
59
Views
33K
Undergrad What is the missing number in this number sequence pattern?
  • · Replies 3 ·
Replies
3
Views
3K
MHB Min(a, b) expressed in terms of absolute value
  • · Replies 17 ·
Replies
17
Views
28K
MHB Solving 8 Roots: Can 3 Quadratic Polynomials Fulfill $f(g(h(x)))=0$?
  • · Replies 1 ·
Replies
1
Views
1K
MHB No Real Zeroes of $x^6-x^5+x^4-x^3+x^2-x+\dfrac{3}{4}$
  • · Replies 1 ·
Replies
1
Views
1K
MHB Find the exact sum of the series 1/(1⋅2⋅3⋅4)+1/(5⋅6⋅7⋅8)+....
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Union of Prime Numbers & Non-Powers of Integers: Usage & Contexts
  • · Replies 1 ·
Replies
1
Views
2K