Rationalising the Denominator Flashcards

The process of eliminating surds from the denominator of a fraction by multiplying numerator and denominator by a suitable value.

An irrational number that cannot be simplified to remove the square root (e.g., √2, √3).

To simplify expressions and make them easier to work with, as required in GCSE Mathematics.

Multiply numerator and denominator by the surd in the denominator (e.g., for 1/√2, multiply by √2/√2).

Multiply by √2/√2 to get √2/2.

Multiply numerator and denominator by the conjugate of the denominator (e.g., (a - √b)/(a - √b)).

A binomial expression where the sign between two terms is reversed (e.g., the conjugate of (a + √b) is (a - √b)).

Multiply by (2 - √3)/(2 - √3) to get (2 - √3)/(4 - 3), which simplifies to (2 - √3).

Multiply by (3 + √5)/(3 + √5) to get (3 + √5)/(9 - 5), which simplifies to (3 + √5)/4.

When multiplying by the conjugate, the denominator becomes a difference of two squares (a² - b²).