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It is irrational
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Is the sum of 18 plus the square root of 10 rational oris the sum of 18 plus the square root of 10 rational or irrational?
It is irrational.
Is the square root of 2 plus the square root of 8 a rational or irrational number?
irrational
Is 814 plus the square root of 99 rational?
No. 1) The square root of any positive integer that doesn't happen to be a perfect square is IRRATIONAL.2) If you add a rational and an irrational number, the result is irrational.
Is 7 plus the square root of 5 irrational and why?
7 plus the square root of 5 is an irrational number because the square root of 5 is a never ending decimal number that can't be expressed as a fraction.
Is 1 plus the square root of 7 rational or irrational?
The square root of any positive integer can only be a WHOLE NUMBER or IRRATIONAL, so the square root of 7 is irrational.On the other hand, the sum of a rational and an irrational number is always irrational.
Is the sum of 18 plus the square root of 10 rational or irrational?
As √10 is irrational, 18 + √10 is irrational.
Is square root of 49 irrational?
No. The square root of 49 is plus or minus 7, both of which are integers. And integers are rational numbers - whether they are positive or negative.
Is a rational plus an irrational equals a rational?
No. A rational plus an irrational is always an irrational.
Why an irrational number plus an irrational number equal a rational?
Well, darling, when you add two irrational numbers together, they can sometimes magically cancel each other out in such a way that the sum ends up being a rational number. It's like mixing oil and water and somehow getting a delicious vinaigrette. Math can be a wild ride, honey.
Is the square root of 49 irrational?
No. The square root of 49 is plus or minus 7, both of which are integers. And integers are rational numbers - whether they are positive or negative.
Is 5 plus the square root of 7 rational or irrational?
The number 5 plus the square root of 7 is irrational. A number is considered rational if it can be expressed as a ratio of two integers, while an irrational number cannot be expressed in this form. Since the square root of 7 is not a perfect square and cannot be simplified to a rational number, the sum of 5 and the square root of 7 is irrational.
How is the sum of a rational and irrational number irrational?
This can easily be proved by contradiction. Without loss of generality, I will take specific numbers as an example. The proof can easily be extended to any rational + irrational number. Assumption: 1 plus the square root of 2 is rational. (It is a well-known fact that the square root of 2 is irrational. No need to prove it here; you can use any other irrational number will do.) This rational sum can be written as p / q, where "p" and "q" are whole numbers (this is basically the definition of a "rational number"). Then, the square root of 2, which is equal to the sum minus 1, is: p / q - 1 = p / q - q / q = (p - q) / q Since the difference of two whole numbers is a whole number, this makes the square root of 2 rational, which doesn't make sense.
