If \(\left( { x }^{ \frac { 1 }{ 2 } }+{ x }^{ -\frac { 1 }{ 2 } } \right) ^{ 2 }=\frac { 9 }{ 2 } \), then find the value of \(\left( { x }^{ \frac { 1 }{ 2 } }-{ x }^{ -\frac { 1 }{ 2 } } \right) \)for x > 1

Classify each element of \(\left\{ \sqrt { 7 } ,\frac { -1 }{ 4 } ,0,3.14,4,\frac { 22 }{ 7 } \right\} \) as a member of N, Q, R, -Q or Z.

Prove that \(\sqrt { 3 } \) is an irrational number. (Hint: Follow the method that we have used to prove \(\sqrt { 2 } \notin Q\))

Are there two distinct irrational numbers such that their difference is a rational number? Justify.

Find two irrational numbers such that their sum is a rational number. Can you find two irrational numbers whose product is a rational number

Find a positive number small than \(\frac { 1 }{ { 2 }^{ 1000 } } \). Justify.

Simplify by rationalising the denominator \(\frac { 7+\sqrt { 6 } }{ 3-\sqrt { 2 } } \)

Solve for x  \(\left| 3-\frac { 3 }{ 4 } x \right| \le \frac { 1 }{ 4 } \)

Compute \({ log }_{ 9 }^{ 27 }-{ log }_{ 27 }^{ 9 }\)

Solve log₈ x + log₄ x + log₂ x = 11