Question

Consider numbers of the form a + b*sqrt(c), where a,b, and c are all rational numbers....

Consider numbers of the form a + b*sqrt(c), where a,b, and c are all rational numbers. express sqrt(a + b*sqrt(c)) in the same form, (i.e. as d + e*sqrt(c)). For which values of c can this be done?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Show that the set of all rational numbers of the form n/5, where n is an...
Show that the set of all rational numbers of the form n/5, where n is an integer, is countable?
Show that the set of all rational numbers of the form n/5, where n is an...
Show that the set of all rational numbers of the form n/5, where n is an integer, is countable?
1. a) Express z = −i−sqrt(3) in the form r cis θ, where θ= Argz, and...
1. a) Express z = −i−sqrt(3) in the form r cis θ, where θ= Argz, and then use de Moivre’s theorem to find the two square roots of −4i. b) Consider: i) p(z)=iz^2+z^3+2iz−2z^2+2z. Given that z=2−2i is a zero of this polynomial, find all of its zeros. ii) p(z)=z^3−2z^2+9z−18. Factorise into linear factors.
An ‘efficient’ market is defined as a market where there are large numbers of rational, profit...
An ‘efficient’ market is defined as a market where there are large numbers of rational, profit ‘maximisers’ actively competing, with each trying to predict future market values of individual securities, and where important current information is almost freely available to all participants. In an efficient market, competition among the many intelligent participants leads to a situation where, at any point in time, actual prices of individual securities already reflect the effects of information based both on events that have already...
Which of the following decimal numbers are rational? A. 0.266266662... from this point on 2s are...
Which of the following decimal numbers are rational? A. 0.266266662... from this point on 2s are separated by increasing even numbers of 6s. B. 0.3333733337... from this point on digits are all 3s except every fifth digit is a 7. C. 0.123455555... from this point on digits are all 5s D.0.10010001001... from this point on the digits are 1s separated by zeros. The number of zeros between the 1s alternates between two and three.
Consider the below 2x2 normal form game. Player 2 C D Player 1 A 5,2 1,3...
Consider the below 2x2 normal form game. Player 2 C D Player 1 A 5,2 1,3 B 4,3 2,1       Assume that Player 1 plays A with p probablity and B with (1-p) probability as Player 2 plays C with q probability and D with (1-q). Given that players are rational, which of the following is true? a. If p = 1/2, then Player 2 Plays C. b. If p =2/3, then Player 2 Plays D. c. If q =1/4,...
1. a. Consider the definition of relation. If A is the set of even numbers and...
1. a. Consider the definition of relation. If A is the set of even numbers and ≡ is the subset of ordered pairs (a,b) where a<b in the usual sense, is ≡ a relation? Explain. b. Consider the definition of partition on the bottom of page 18. Theorem 2 says that the equivalence classes of an equivalence relation form a partition of the set. Consider the set ℕ with the equivalence relation ≡ defined by the rule: a≡b in ℕ...
Phospholipids can form all the following structures in a water environment except? a)chloroplasts b) bilayers c)...
Phospholipids can form all the following structures in a water environment except? a)chloroplasts b) bilayers c) Chromosomes d) Endoplasmic reticulum e) nuclear membrane
Suppose you have two numbers x, y ∈ Q (that is, x and y are rational...
Suppose you have two numbers x, y ∈ Q (that is, x and y are rational numbers). a) Use the formal definition of a rational number to express each of x and y as the ratio of two integers. Remember, x and y could be different numbers! (b) Use your results from (a) to show that xy must also be a rational number. Carefully justify your answer, showing how it satisfies the formal definition of a rational number. (2) Suppose...
1) Define p-values in the form of a conditional probability, i.e. p-value = Prob(A|B) where you...
1) Define p-values in the form of a conditional probability, i.e. p-value = Prob(A|B) where you say what A and B are 2) Define likelihood (from the likelihood ratio test) in the form of a conditional probability, i.e. likelihood = Prob(A|B) where you say what A and B are