Integrated Mathematics

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Presentation transcript:

Integrated Mathematics Surds

Irrational Number Number that cannot be expressed as a fraction of two integers

x x x Think! Which of the following is NOT a irrational number?

Rules of Indices and Surds

Simplify

Simplify

Simplify

Simplify

Simplify

Rationalization of the Denominator Process of removing a surd from the denominator Example:

Objective is to remove surds from denominator Example: Note! Multiple together! Objective is to remove surds from denominator Conjugate Surds

Re-look into the question: Multiply conjugate surds Multiply denominator and numerator

Rationalize the denominators: Multiply conjugate surds Multiply denominator and numerator

Rationalize the denominators: Multiply conjugate surds Multiply denominator and numerator

Rationalize the denominators: Multiply conjugate surds Multiply denominator and numerator

Rationalize the denominators: Multiply conjugate surds Multiply denominator and numerator

Rationalize the denominators: Multiply conjugate surds Multiply denominator and numerator

Multiply denominator and numerator Rationalize the denominators: Determine the LCM Multiply denominator and numerator

Expand the denominators Rationalize the denominators: Expand the denominators Find the LCM

Rationalize the denominators: Same denominator Rationalization