Algebra, Algebraic Techniques, Multiplication by the Conjugate

Multiplication by the conjugate is an algebraic technique used to simplify expressions, especially fractions with radicals or complex numbers in the denominator. For an expression like `a + \sqrt{b}`, its conjugate is `a - \sqrt{b}`. Questions involve applying this method for rationalization or simplification.

• Question

  Find the value of the expression without a calculator:

  `(sqrt(sqrt(2)-1))/(sqrt(sqrt(2)+1))+ (sqrt(sqrt(3)-sqrt(2)))/(sqrt(sqrt(3)+sqrt(2)))+ (sqrt(2-sqrt(3)))/(sqrt(2+sqrt(3)))`

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  Topics:

  Algebra -> Algebraic Techniques -> Short Multiplication Formulas / Algebraic Identities Algebra -> Algebraic Techniques -> Roots / Radicals Algebra -> Algebraic Techniques -> Multiplication by the Conjugate