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No, 13 is not a rational number. Yes, here's the proof.
Let's start out with the basic inequality 9 < 13 < 16.
Now, we'll take the square root of this inequality:
3 < √13 < 4.
If you subtract all numbers by 3, you get:
0 < √13 - 3 < 1.
If √13 is rational, then it can be expressed as a fraction of two integers, m/n. This next part is the only remotely tricky part of this proof, so pay attention. We're going to assume that m/n is in its most reduced form; i.e., that the value for n is the smallest it can be and still be able to represent √13. Therefore, √13n must be an integer, and n must be the smallest multiple of √13 to make this true. If you don't understand this part, read it again, because this is the heart of the proof.
Readmore:http://wiki.answers.com/Q/Is_the_square_root_of_13_an_irrational_number#ixzz1WjS9rkGp
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Is the square root of 13 irrational or rational?
The square root of 13 is irrational. All square roots of whole numbers are irrational unless the number is a perfect square.
What number is 13 the square root of?
169. 13 x 13 = 169. square root of 169 = 13.
Is the number 13 a square number or a square root of a number?
It is both.13 is the square of +/- 3.6056, approx. However, since it is not the square of an integer, it is not a perfect square.It is also the square root of 169.
What number is 13 a square root of?
169
What is the conjugate of square root of 13?
If the square root of a number is irrational, it is its own conjugate. sqrt(13)*sqrt(13) = 13 and you no longer have an irrational!
Is the square root of 169 a rational or irrational number?
The square root of 169 is 13 which is a rational and also a Prime number
Is the square root of 168 a rational Number?
Yes, the square root of 168 is a rational number. It's 13.
Is the square root 169 a rational number?
Yes, because the square root of 169 is 13 which is a rational number
Is the square root of 169 is rational?
Yes because the square root of 169 is 13 which is a rational number
Is the square root of 13 irrational or rational?
The square root of 13 is irrational. All square roots of whole numbers are irrational unless the number is a perfect square.
Is the square root of 13 is a rational number?
No. The square root of a positive integer is either a whole number or it is irrational.
Is the square root 169 rational?
The square root of 169 is 13
Is the square root of 169 rational?
The square root of 169 is 13
Is the square root of 13 rational?
No - it is an irrational number. Rounded to ten decimal places, it is equal to 3.6055512754.
10 example of rational irrational numbers?
Rational numbers:1, 2, 3, 4, 5, 6, 7, 8, 9, 10Irrational numbers:square root of (2)square root of (3)square root of (5)square root of (6)square root of (7)square root of (8)square root of (10)square root of (11)square root of (12)square root of (13)
What number is 13 the square root of?
169. 13 x 13 = 169. square root of 169 = 13.
Is a square root a rational number?
A square root is considered a rational number if the number inside the square root sign is a perfect square. In other words, if the square root of a number results in a whole number, then it is a rational number. For example, the square root of 9 is 3, which is a whole number, making it a rational number. However, if the square root results in a non-terminating, non-repeating decimal, then it is considered an irrational number.
