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Q: How can you prove that the square root of three is an irrational number?

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The square root of nine is three, and that is not an irrational number.

No, it is an irrational number.

The square root of 15 is an irrational number and it is about 3.873 rounded to three decimal places

Any number that can't be expessed as a fraction is an irrational number as for example the square root of 4.5

pi, e, most square roots.

The square roots of three are examples of irrational numbers.

The square root of 221 is an irrational number and it is about 14.866 rounded to three decimal places

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It is an irrational number and it is about 1.077 to three decimal places.

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The square root of 163 is - approximately - 12.7671453348037 As this is a number which cannot be expressed as a fraction it is called an irrational number.

Yes. It would be 21/2 * 91/2, or "three root two". Root two is an irrational number, so it's products - such as root 18, will be as well.

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No. The square root of 81/(-3) is rational. The square root of [81/(-3)] is imaginary (a kind of complex number).

The square root of 14 is irrational. Three squared is 9, and four squared is 16; so square root of 14 is in-between 3 and 4.

No.

No. The square root of three is an irrational number. That means that it cannot be represented as a fraction. Any terminating decimal can be represented as a fraction with some power of 10 in the denominator.

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Negative three is a rational number.

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Yes.