answersLogoWhite

0


Best Answer

It is irrational, here's the proof.

Let's start out with the basic inequality 49 < 50 < 64.

Now, we'll take the square root of this inequality:

7< √50 < 8.

If you subtract all numbers by 7, you get:

0 < √50 - 7 < 1.

If √50 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 √50. Therefore, √50n must be an integer, and n must be the smallest multiple of √50 to make this true. If you don't understand this part, read it again, because this is the heart of the proof.

Now, we're going to multiply √50n by (√50 - 7). This gives 50n - 7√50n. Well, 50n is an integer, and, as we explained above, √50n is also an integer, so 7√50n is an integer too; therefore, 50n - 7√50n is an integer as well. We're going to rearrange this expression to (√50n - 7n)√50 and then set the term (√50n - 7n) equal to p, for simplicity. This gives us the expression √50p, which is equal to 50n - 7√50n, and is an integer.

Remember, from above, that 0 < √50 - 7 < 1.

If we multiply this inequality by n, we get 0 < √50n - 7n < n, or, from what we defined above, 0 < p < n. This means that p < n and thus √50p < √50n. We've already determined that both √50p and √50n are integers, but recall that we said n was the smallest multiple of √50 to yield an integer value. Thus, √50p < √50n is a contradiction; therefore √50 can't be rational and so must be irrational.

Q.E.D.

User Avatar

Wiki User

13y ago
This answer is:
User Avatar
More answers
User Avatar

Wiki User

7y ago

√50 is irrational.

This answer is:
User Avatar

User Avatar

Wiki User

12y ago

Irrational.

This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: Is the square root of 50 irrational or rational?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

The square root of 50 is it rational or irrational?

The square roots of 50 are irrational.


Is the square root of 50 an irrational or rational number?

irrational


Is the square root of a 50 a rational number?

The square root of 50 is roughly 7.071067812, which is irrational.


Is the square root of 50 irrational or rational and is it a perfect square?

The square root of 50 is an irrational number because it can't be expressed as a fraction.


What is the square root of 50 turned into fraction?

The square roots of 50 are irrational numbers. You cannot turn irrational numbers into fractions, which are rational numbers.


Is the square root of 50 irrational or a rational number?

The square root of 50 is an irrational number. Irrational numbers are real numbers that cannot be expressed as a fraction a/b where a and b are integers and b is non-zero. Rational numbers are numbers that can be expressed as a fraction a/b where a and b are integers and b is not zero. The square root of 50 is approximately 7.071067812, which cannot be expressed as a fraction of integers. For example, the square root of 50 is between 7 and 71/100, but even (707110/100000)2 is approximately 50.00045521, which is still not quite 50.


Is the square root of 50 a rational or irrational?

The square root of 50 is an irrational number. Irrational Numbers are real numbers that cannot be expressed as a fraction a/b where a and b are integers and b is non-zero. Rational numbers are numbers that can be expressed as a fraction a/b where a and b are integers and b is not zero. The square root of 50 is approximately 7.071067812, which cannot be expressed as a fraction of integers. For example, the square root of 50 is between 7 and 71/100, but even (707110/100000)2 is approximately 50.00045521, which is still not quite 50.


Is the square root of 50 an irrational number?

Yes


Square root of 5000?

It is an irrational number in the form of 50 times the square root of 2


Is 50 irrational?

50 is a rational number


Is the square root of 50 rational?

No, the sqrt of 50 is sqrt (25 x 2) = sqrt 25 x sqrt 2 = 5 x sqrt 2. Sqrt 2 is irrational.


What is an irrational number between 0.11 and 0.12?

The square root of .014 is about .118322. Note that .014 is 14/1000 which is 7/500 this is the (square root of 35)/50 which is an irrational number.