Rational or irrational? 10 pts!!?

Question

Determine which are rational and which are irrational.

1. The square root of negative 49

2. -0.733
and. __
3. 6.527

Thanks!! =)
p.s. :The repeating sign on question 3 is supposed to be over the 2 and the 7.

Answer 1

The first one is imaginary. Imaginary numbers are not real numbers, therefore not rational or irrational. Is your teacher giving you a trick question? :)

As the others have said, numbers 2 and 3 are both rational.

Answer 2

1. √-49 is 7i, which is imaginary, so this depends on what we really mean by a "rational number". You can't express 7i as a/b where a and b are both integers, because you still have that "i" to deal with. So it would seem that 7i is therefore irrational by default. However, "rational" and "irrational" really only apply to real numbers, so the answer here is "neither".

2. This is a decimal that terminates, so it is rational.

3. This is a decimal that repeasts, so it is rational.

Remember there are two equivalent definitions of a rational number: a number that can be expressed as a/b where a and b are integers, and a number whose decimal terminates or repeats. This is because you can always convert a number with a terminating or repeating decimal as a fraction.

Answer 3

1. The square root of negative 49 = 7i, complex rational number

2. Rational

3. Rational

This numbers can be all be written in the form p/q where p and q are numbers. An irrational number is one that it's infinitly long and never repeats any number pattern.

Square Root of 2 it's an irrational number for example.

Answer 4

Hey there!

The first one is supposed to be a rational complex number, or a rational imaginary number. 7i and -7i are an example of it. -0.733 is rational, since the decimal terminates, or stops at a specific place. 6.527 is rational, since the decimal digits repeat.


ADDITION: Gary H was correct. With some twist in his words, all rational numbers are real numbers. But all rational numbers are not imaginary numbers. The rational numbers are not a subset of imaginary numbers. So the first one is neither.

Hope it helps!

Answer 5

1) The square root of negative 49

No real solution, as in neither rational or irrational! -Requires a complex number (the set of real numbers is the sum of the set of rational and irrational numbers)

2) -0.733 Definitely rational, equals -733/1000

3) 6.5272727... is rational, like all repeating decimals it can be expressed as a fraction with integer numerator and denominator.

Trust me.

Answer 6

#1 is imaginary, not irrational (the answer is +/- 7i, where i is the imaginary square root of -1). #2 is rational. #3 is rational - all terminating and repeating decimals are rational.

Answer 7

An irrational number has an infinite number of decimals without any repeating parts. None of the three numbers is irrational.

Answer 8

1. √(-49) = irrational (± 7i, an imaginary number)
Only the square roots of square (real) numbers are rational.

2. -0.733 = rational
The digits terminate at the second 3.

3. 6.527272727 = rational
Repeating digits.

Answer 9

1. irrational (technically it's imaginary not irrational)
2. rational
3. rational

Answer 10

1. irrational it would be 7i and thats imaginary
2. rational repeats
3. rational repeats