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It is a Prime number that has only factors of itself and one therefore it is an irrational number like all prime numbers are.

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Q: Give a proof that the square root of 3 is an irrational nu?

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Most high school algebra books show a proof (by contradiction) that the square root of 2 is irrational. The same proof can easily be adapted to the square root of any positive integer, that is not a perfect square. You can find the proof (for the square root of 2) on the Wikipedia article on "irrational number", near the beginning of the page (under "History").

The square root of a positive integer can ONLY be:* Either an integer, * Or an irrational number. (The proof of this is basically the same as the proof, in high school algebra books, that the square root of 2 is irrational.) Since in this case 32 is not the square of an integer, it therefore follows that its square root is an irrational number.

No, the square root of 3 is not rational.No. The square root of 3 is irrational.More generally: if p is a prime number then the square root of p is irrational and the proof of this fact mimics the famous proof of irrationality of the square root of 2.No - the square root of 3 is not rational, but the proof is too involved to post here.

Yes. For example, the square root of 3 (an irrational number) times the square root of 2(an irrational number) gets you the square root of 6(an irrational number)

The square root of 200 is irrational.

Yes. The square root of a positive integer can ONLY be either:* An integer (in this case, it isn't), OR * An irrational number. The proof is basically the same as the proof used in high school algebra, to prove that the square root of 2 is irrational.

irrational square root of 121 = 11 square root of 1.21 = 1.1 square root of 12.1 = 3.47...

Search for the proof for the irrationality of the square root of 2. The same reasoning applies to any positive integer that is not a perfect square. In summary, the square root of any positive integer is either a whole number, or - as in this case - it is irrational.

The square root of 94 is an irrational number

[ square root of (4.1) ] is irrational. But [ square root of (4) ] is rational.

The square root of 29 is an irrational number.

It is a irrational number. Because the square root of every imperfect square is irrational number.

An irrational number is a number that never ends. An example of an irrational square root would be the square root of 11.

square root of (2)

If the positive square root (for example, square root of 2) is irrational, then the corresponding negative square root (for example, minus square root of 2) is also irrational.

sqrt(8) = sqrt(4*2) = 2*sqrt(2).Even without given that sqrt(2) is a rational, you can give that the square root of 2 starts converging onto the "Pythagoras Constant" eventually, as it takes an infinite amount of digits to square root an integer that is not perfectly squared.Thus, an rational x irrational = irrational, thus the sqrt(8) is irrational (an approximation is 2.8284271247...).

Yes, square root of 33 is irrational.

The square root of 12 is an irrational number

The square root of 2.5 is irrational

The square root of 254 can be said to be irrational.

The square root of 37 is an irrational number.

The square root of 0.144 is an irrational number

The square root of 12 is an irrational number

The square root of (any number that isn't a perfect square) is irrational.

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.