Q: Is the sum of 2 plus the square root of 2 irrational?

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It is 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.

As √10 is irrational, 18 + √10 is irrational.

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.

That simply isn't true. The sum of two irrational numbers CAN BE rational, but it can also be irrational. As an example, the square root of 2 plus the square root of 2 is irrational.

The sum, or difference, of two irrational numbers can be rational, or irrational. For example, if A = square root of 2 and B = square root of 3, both the sum and difference are irrational. If A = (1 + square root of 2), and B = square root of 2, then, while both are irrational, the difference (equal to 1) is rational.

Yes.

I'm assuming that you mean 'square root'. Yes, this sum is irrational. So are each of the two numbers alone. A simple proof can be done by writing x=square root 2 + square root 3 and then "squareing away" the square roots and then use the rational roots theorem. The sum or difference of two irrational number need not be irrational! Look at sqrt(2)- sqrt(2)=0 which is rational.

just give me an answer! K? Thanks!

Square root of 2 = 1.414213562... Square root of 7 = 2.645751311... The sum is 4.059964873...

You can. Just add the numbers together, and find their square root. One plus three is four; the square root of the sum is two.

Yes, for example: square root of 2, and the negative of the square root of 2.

Assuming the roots are positive, then ~ 15.59.

It is an irrational number that can't be determined or expressed as a fraction.

It's not. Take 49 and 16 for example. The square root of the sum is the square root of 65. The sum of the square roots is 11.

example for sum of rational numbers is 1/3 + 1/5 Example for sum of irrationals is Pi + e where e is is base of natural log Another is square root of 2 + square root of 3.

to find the root-sum square of n numbers you square each number, add them, then take square root of sum For exanple root sum square of 2,3, and 4 is square root of (4+9+16) = sqrt(29) = 5.39

The numbers are: 6 plus square root of 27 and 6 minus square root of 27

The sum of a number plus 3 to the square root of 9 to the sum of 2 would equal -2. This is a math problem.

I would say 19 as the square root of 9 is 3, plus 16, makes 19. I would assume the questioner expects many people to answer 5 which is the square root of the sum of 9 and 16.

false

Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always 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.

No. The sum of an irrational number and any other [real] number is irrational.

It's an example of "addition".The sum is: 2 sqrt(34) .

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