Which of the following is a rational number?

Every rational number is:

A rational number lying between \(\sqrt { 2 } \) and \(\sqrt { 3 } \) is:

The rational number between -1/5 and -2/5 is

Which of the following numbers is an irrational number?

The sum of \(0.\overline { 3 } \) and \(0.\overline { 2 } \)

(0.001)^1/3 is equal to

If \({ 8 }^{ x }=\frac { 64 }{ { 2 }^{ x } } \) , then the value of x is

State whether the following statements are true or false.Give reason for your answer.
(i) Every whole number is a natural number.
(ii) Zero is neither a negative nor a positive integer.
(iii) There are finitely many rational numbers between any two given rational numbers.

Are the following statements true or false? Justify your answers. 
(i) Every real number is either irrational or rational.
(ii) \(\sqrt { 7 } \)  is an irrational number but not a real number.
(iii) 4 is real but not irrational

Find two rational numbers between 0.1 and 0.2.

Write three rational numbers between -2/5 and -1/5.

Find five rational numbers between 1 and 2.

Express \(18.\overline{48} \) in the form of p/q, where p and q are integers, \(q\neq 0\) .

Check whether \(7\sqrt { 5 } ,\frac { 7 }{ \sqrt { 5 } } .\sqrt { 2 } +21,\pi -5\) are irrational numbers or not.

Divide \(8\sqrt { 15 } \) by \(2\sqrt { 3 } \)

If \(a=\frac { 2-\sqrt { 5 } }{ 2+\sqrt { 5 } } \) and \(b=\frac { 2+\sqrt { 5 } }{ 2-\sqrt { 5 } } \), then find \({ \left( a+b \right) }^{ 3 }\)

If \(p=\frac { 3-\sqrt { 2 } }{ 3+\sqrt { 2 } } \) and \(q=\frac { 3+\sqrt { 2 } }{ 3-\sqrt { 2 } } \) find \({ p }^{ 2 }+{ q }^{ 2 }\)

Simplify: \({ \left[ { 5 }^{ 2 }{ \left( { 8 }^{ 1/3 }+{ 27 }^{ 1/3 } \right) }^{ 3 } \right] }^{ 1/5 }\)

Write the following in decimal form and say what kind of decimal expansion each has:
\(\frac { 3 }{ 13 } \)

Simplify: \(3\sqrt { 45 } -\sqrt { 125 } +\sqrt { 200 } -\sqrt { 50 } \)

(i) express 2.4 \(\overline { 248 } \) in the form of \(p\over q\) where \(p\over q\) is in its lowest form.
(ii) What is the value of p?
(iii) what is the value of q?
(iv) what name can be given to the number p?
(v) what name can be given to the number q?
(vi) Apala declares that p and q are co-prime. IS she correct? If so, which value of Apala is depicted by her declaration?
(vii) Which mathematical concept has been converted in this problem?
(viii) Write the formulae used in the solution.

Prove that \(\frac { { 2 }^{ 30 }+{ 2 }^{ 29 }+{ 2 }^{ 28 } }{ { 2 }^{ 31 }+{ 2 }^{ 30 }+{ 2 }^{ 29 } } =\frac { 7 }{ 10 } \)