about irrational numbers?

Question

if x and y are irrational numbers; what can be said about x raise to the power y
a) always irrational
b)sometimes rational sometimes irrational
c)will be rational only if x.y = irrational
d)will be irrational only if x.y=rational
explain answers

Answer 1

The usual proof that it can be rational is to take the example:

u = sqrt(2) ^ sqrt(2).

Now, u is an irrational to an irrational power. If u is irrational, then:

v = u ^ sqrt(2) = (sqrt(2) ^ sqrt(2)) ^ sqrt(2)
= sqrt(2) ^ (sqrt(2) * sqrt(2)) = sqrt(2) ^ 2 = 2.

So, either u is rational and we have an irrational to an irrational power is rational. If u is irrational, then u ^ sqrt(2) is an example of an irrational to an irrational power being irrational.

Answer 2

A, because raising something to an irrational power is like multiplying the number by itself an irrational number of times

Answer 3

355/113 will recur with a era of length decrease than 113. The definition wins right here and says that 355/113 is rational. the subject is in assuming that 355/113, which superficially imitates pi partly of its decimal representation, does not terminate. yet another concern is interior the fact that the rationals and irrationals are disjoint instruments via their definitions. i'm curious as to why you theory that 355/113 does not recur?

Answer 4

If x and y are irrational, then x^y may be rational or irrational.
So the answer is (b).

Answer 5

It has to be always irrational, as any number raised to the power of any irrational number is irrational number.

Answer 6

The correct answer is
b) some times rational, some times irrational.
a) is false since (sqrt2)^(sqrt2) is irrational and
[(sqrt2)^(sqrt2)]^(sqrt2) = 2 is rational.
c) is false since if x = (sqrt2) , y = (sqrt3) then xy is irrational and
x^y is also irrational.
d) is false as the same example in c) holds.

Answer 7

Irrational numbers are strange answers to math problems from people who don't understand math very well.

:o)

Answer 8

irrational bcoz to multiply a number to its power,the power must be defined first

Answer 9

if you what is irrational no. then you must know that it can't be solved.
if you thing it can be solved give me an example
(b)you can say sometimes rational sometimes irrational.

i.e. option (b.)

Answer 10

a) is wrong because x in x^x = 5, x is irrational.
c) is wrong because sqrt(2) ^ 2 = 2
d) is wrong because 2^2 = 4

Therefore the answer must be b.