0
Still curious? Ask our experts.
Chat with our AI personalities
Rafa
Devin
JudyAdd your answer:
Earn +20 pts
Are the products of irrational numbers always irrational?
No. The product of conjugate pairs is always rational.So suppose sqrt(y) is the irrational square root of the rational number y. ThenThus [x + sqrt(y)]*[x - sqrt(y)] = x^2 + x*sqrt(y) - x*sqrt(y) - sqrt(y)*sqrt(y)= x^2 + y^2 which is rational.
What is an irrational number and examples?
An irrational number is a number that cannot be written as a ratio of two whole numbers. That is, there are no two integers, X and Y (with Y>0) such that the number can be written as X/Y. Sqrt(2), pi, log(3) are examples of irrational numbers.
Why is the sum of a rational numbers and an irrational number is irrational?
Let x be a rational number and y be an irrational number.Suppose their sum = z, is rational.That is x + y = zThen y = z - xThe set of rational number is closed under addition (and subtraction). Therefore, z - x is rational.Thus you have left hand side (irrational) = right hand side (rational) which is a contradiction.Therefore, by reducio ad absurdum, the supposition that z is rational is false, ie the sum of a rational and an irrational must be irrational.
Is the product of rational no and irrational no is rational?
Unless you multiply 0 with some irrational number, it is impossible. Here's why: Let x,y be rational with x = a/b, z = c/d and y be the irrational number. If we presume xy = z then we have y = z/x. However, this is equal to (c/d)/(a/b) = (bc)/(ad), which is rational. Since y is assumed to be irrational, this cannot occur (unless one of b,c is zero).
Is 4 Over 4 An Irrational Number?
No. 4 over 4, or 1 whole, is not an irrational number. It can be written as a simple fraction, 4/4, so it is not an irrational number.
