Which of the following is a rational number?

Every rational number is:

A rational number lying between -3 and 3 is:

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

Two rational numbers between \(\frac { 2 }{ 3 } \) and \(\frac { 5 }{ 3 } \)are:

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

Is \(\frac{\sqrt{98}}{\sqrt{2}}\) a rational number or not?

Write a real number which has terminating decimal expansion.

Insert three rational numbers between \(\frac{-1}{3}\) and \(\frac{-2}{3}\)

Are the following statements true or false? Give reasons for your answers.
(i) Every whole number is a natural number.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.

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

Simplify: 17².17^-5

Simplify the following expressions:
\((i)\ (5+\sqrt { 7 } )(2+\sqrt { 5 } )\)
\((ii)\ (5+\sqrt { 5 } )(5-\sqrt { 5 } )\)
\((iii)\ { \left( \sqrt { 3 } +\sqrt { 7 } \right) }^{ 2 }\)
\(\\ (iv)\left( \sqrt { 11 } -\sqrt { 7 } \right) \left( \sqrt { 11 } +\sqrt { 7 } \right) \)

Rationalize \(\frac { 5 }{ \sqrt { 3 } -\sqrt { 5 } } \left( -\frac { 5 }{ 2 } \right) \)

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 \(x=\frac { \sqrt { 3 } +\sqrt { 2 } }{ \sqrt { 3 } -\sqrt { 2 } } \) and \(y=\frac { \sqrt { 3 } -\sqrt { 2 } }{ \sqrt { 3 } +\sqrt { 2 } } \) , find the value of \({ x }^{ 2 }+{ y }^{ 2 }+xy\)

Simplify \(\frac { 1 }{ 1+\sqrt { 2 } } +\frac { 1 }{ \sqrt { 2 } +\sqrt { 3 } } +\frac { 2 }{ \sqrt { 3 } +\sqrt { 5 } } \)

Find the value of x if \({ 2 }^{ 4 }\times { 2 }^{ 5 }={ \left( { 2 }^{ 5 } \right) }^{ x }\)

Find the product of 5√2(3 + √2)(5 + √2)

Is zero a rational number?can you write it in the form \(\frac { p }{ q } \),where p and q are integers and \(q\neq 0\)?

State whether the following statements are true or false.Give reasons for your answers.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.

Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

Write the following in decimal form and say what kind of decimal expansion each has:
\(\frac { 36 }{ 100 } \)

Find three different irrational numbers between the rational numbers \(\frac { 5 }{ 7 } \) and \(\frac { 9 }{ 11 } \)

Find two rational numbers in the form \(\frac { p }{ q } \) between 0.34 344 3444 3... and 0.36 366 3666 36666 3...

Find two irrational numbers between 2 and 2.5.

Express \(0.\overline { 235 } \) in the form of \(\frac { p }{ q } \) where p and q are integers and \(q\neq 0\)

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

Show that: \(\frac { 1 }{ 1+{ x }^{ a-b } } +\frac { 1 }{ 1+{ x }^{ b-a } } =1\)

Geetha told her classmate Radha that "\(\sqrt { \frac { \left( \sqrt { 2 } -1 \right) }{ \left( \sqrt { 2 } +1 \right) } } \) is an irrational number." Radha replied that "you are wrong" and further claimed that "If there is a number 'x' such that x³ is an irrational number, then x⁵ is also irrational". Geetha said, "No Radha, you are wrong". Radha took some time and after verification accepted her mistakes and thanked Geetha for pointing out these mistakes. 
(i) Justify both the statements.
(ii) What value is depicted from this question?