Rationalize the surds of the denominator:

Find the simplest value of:

7√11 is an ___ number.

If the sum of the square of the roots of the equation 6x² + x + k = 0 is , then the value of k is 12.

If mean proportional of (a2bc) and (4bc) is x, then the value of x is _____.

If a = and ab = 1 calculate ( + )

If m + = √3, then find the value of (a) m² + and (b) m³ + .

If x + √(x² - 9) = 9 then find the value of x - √(x² - 9).

If x = , then find the value of +

If x(4 - √3) = y(4 + √3) = 1, then the value of x² + y² = ______

If x = √3 + √2 and y = 1/x then find (x + )² + ( - y)²

Which one is greater √7 - √2 or √8 - √3?