If \(x={ \left( 2+\sqrt { 5 } \right) }^{ \frac { 1 }{ 2 } }+{ \left( 2-\sqrt { 5 } \right) }^{ \frac { 1 }{ 2 } }\) and \(y={ \left( 2+\sqrt { 5 } \right) }^{ \frac { 1 }{ 2 } }-{ \left( 2-\sqrt { 5 } \right) }^{ \frac { 1 }{ 2 } }\) , then evaluate \({ x }^{ 2 }+{ y }^{ 2 }\)

Recall, \(\pi \) is defined as  the ratio of circumference of a circle to its diameter. This seems to contradict the fact that \(\pi \) is irrational.How will you resolve this contradiction?

Simplify each of the following expressions: \({ \left( \sqrt { 5 } +\sqrt { 2 } \right) }^{ 2 }\)

Express the following in the form p/q, where p and q are integers and \(q\neq 0\)
\(0.\overline { 47 } \)

Write the following in decimal form and say what kind of decimal expansion each has:
\(4\frac { 1 }{ 8 } \)

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.

Express the decimal number \(2.\overline { 218 } \) in the form of \(\frac { p }{ q } \) where p and q are integers and \(q\neq 0\)

Find two irrational numbers between \(\frac { 1 }{ 3 } \)and \(\frac { 1 }{ 2 } \)

Find three rational numbers between \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 2 } \) .How many rational numbers can be determined between these two numbers?

Simplify 2^2/3 . 2^1/3

Simplify \(\frac { 4\sqrt { 3 } }{ 2-\sqrt { 2 } } -\frac { 30 }{ 4\sqrt { 3 } -3\sqrt { 2 } } -\frac { 3\sqrt { 2 } }{ 3+2\sqrt { 3 } } \)

Simplify: \(\frac { 2+\sqrt { 3 } }{ 2-\sqrt { 3 } } -\frac { 2-\sqrt { 3 } }{ 2+\sqrt { 3 } } \)

If \(x=\frac { \sqrt { 5 } +1 }{ \sqrt { 5 } -1 } ,\quad y=\frac { \sqrt { 5 } -1 }{ \sqrt { 5 } +1 } \) , find the value of \({ x }^{ 2 }+{ y }^{ 2 }+xy\)

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

Show that 0.2353535...\(=0.2\overline { 35 } \) can be expressed in the form p/q, where p and q are integers and \(q\neq 0\)

Express \(0.12\overline { 3 } \) into the form p/q, where p,q are integers and \(q\neq 0\)

Show that 3.142678 is a rational number.In other words, Express 3.142678 in the form p/q where p and q are integers and \(q\neq 0\) .

\(\left( 5+\sqrt { 8 } \right) +\left( 3-\sqrt { 2 } \right) -\left( \sqrt { 2 } -6 \right) \) when simplified is:

The process of visualisation of representation of numbers on the number line through a magnifying glass is called

The decimal form of 56/1000 is

Every rational number is: