The conjugate surd of root 2 minus 1
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if simplification of the complex surd 63√−1 is to be done, denominator 3–√−1 is to be converted to a rational number. If a = 3–√ and b = 1, then denominator is (a-b), if we multiply (a + b) or 3–√+1, it will a2−b2 and 3–√ will be squared off.
63√−1
= 6(3√+1)(3√−1)(3√+1)
= 6(3√+1)3−1
= 6(3√+1)2
= 2(\sqrt{3} + 1).
In the above example 3–√+1 is used as rationalizing factor which is a conjugate to 3–√−1.
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