Yes.
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Yes, two thirds is a rational number. This is because it a is recurring decimal and can be expressed as a fraction. All fractions are rational numbers and all recurring decimals are rational numbers.
Every positive rational number and its negative are the two square roots of the same positive rational number.
2/3 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Yes. A number is called a rational number if it can be written as the ratio of two integers. (-6) and 1 are both integers. -6 = -6/1. Therefore -6 is a rational number. Rational numbers can be either positive or negative (zero is also a rational number).
It would be 21 and two thirds, so it can be expressed as a fraction and is therefore rational.