Yes. The square root of a natural number (positive integer) is either an integer, or an irrational number.
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irrational
No because it is 2 times the square root of 21 which is an irrational numberThe square root of 84 is not a rational number
Yes, albeit 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.
4.6 is a better approximation to the square root of 21.