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Conjugate Surd
Conjugate Surd
Every binomial surd (a√ b + c√ d) has a conjugate counterpart (a√ b − c√ d). A property of the conjugate surd is that when you multiply a surd with its conjugate, the product will be a rational number (See Table below).
Every binomial surd (a√ b + c√ d) has a conjugate counterpart (a√ b − c√ d). A property of the conjugate surd is that when you multiply a surd with its conjugate, the product will be a rational number (See Table below).
This is useful for rationalising fractions with surds in the denominators.
This is useful for rationalising fractions with surds in the denominators.
Example
Example
Test Yourself!
Test Yourself!
Use the applet below to check your understanding of rationalising a denominator using the conjugate surd.
Use the applet below to check your understanding of rationalising a denominator using the conjugate surd.
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