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

5

(a)

If √2 = 1.414 and √3 = 1.732, then calculate \(\frac { 4 }{ 3\sqrt { 3 } -2\sqrt { 2 } } +\frac { 3 }{ 3\sqrt { 3 } -2\sqrt { 2 } } \)

5

(a)

If \(x=\frac { 1 }{ 3-2\sqrt { 2 } } \) and \(y=\frac { 1 }{ 3+2\sqrt { 2 } } \), then find the value of x + y + xy.

5

(a)

If x = 2 + √3, then find the value of x²+\(\frac{1}{x^{2}}\)

5

(a)

If x = √2-1, then find the value of \((x-\frac{1}{x})^{3}\) .

5

(a)

Find the value of \({ \left( x-\frac { 1 }{ x } \right) }^{ 3 }\) , if x = 1 + √2

5

(a)

If x = 9 + 4√5, then find the value of √x-\(\frac{1}{\sqrt{x}}\)

5

(a)

If \(\frac { 30 }{ 4\sqrt { 3 } +3\sqrt { 2 } } =4\sqrt { 3 } -a\sqrt { 2 } \) find the value of a.

5

(a)

Find the value of a and b if \(\frac { \sqrt { 2 } +1 }{ \sqrt { 2 } -1 } -\frac { \sqrt { 2 } -1 }{ \sqrt { 2 } +1 } \)

5

(a)

If \(\frac { 3 }{ 4\sqrt { 5 } -\sqrt { 3 } } +\frac { 2 }{ 4\sqrt { 5 } +\sqrt { 3 } } =a\sqrt { 5 } +b\sqrt { 3 } \) then find the values of a and b.

5

(a)