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

Find five rational numbers between 1 and 2.

Find two irrational numbers between 0.1 and 0.12.

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 \({ x }^{ 2 }+{ y }^{ 2 }\)

Classify the following numbers as rational or irrational: \(\frac { 2\sqrt { 7 } }{ 7\sqrt { 7 } } \)

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

The simplified form of \(\frac { { 13 }^{ \frac { 1 }{ 5 } } }{ { 13 }^{ \frac { 1 }{ 3 } } } \) is

If \(\sqrt { x } \) is an irrational number, then x is:

Write the rationalizing factor of \(\frac{1}{\sqrt{50}}\) .

Find the value of \(\sqrt[3]{625^{-2}}\)

Is the product of two irrational numbers always an irrational number?

Calculate the decimal which represents the fraction \(\frac{7}{8}\)

Prove that: \({ \left( \frac { { x }^{ { a }^{ 2 } } }{ { x }^{ { b }^{ 2 } } } \right) }^{ \frac { 1 }{ a+b } }.{ \left( \frac { { x }^{ { b }^{ 2 } } }{ { x }^{ { c }^{ 2 } } } \right) }^{ \frac { 1 }{ b+c } }.{ \left( \frac { { x }^{ { c }^{ 2 } } }{ { x }^{ { a }^{ 2 } } } \right) }^{ \frac { 1 }{ c+a } }=1\)