Some of the important rules of surds are listed below.

**1.** Every rational number is not a surd.

**2.** Every irrational number is a surd.

**3.** A root of a positive real quantity is called a surd if its value cannot he exactly determined.

√9, ∛64, ∜(16/81) etc. are rational numbers but not surds because √9 = 3, ∛64 = 4, ∜(16/81) = 2/3 etc.

**4. **√a × √a = a ⇒ √5 × √5 = 5

**5.** The sum and difference of two simple quadratic surds are said to be conjugate surds or complementary surds to each other. Thus, (4√7 + √6) and (4√7 - √6) are surds conjugate to each other.

**6.** To express in the simplest form, denominator must be
rationalized.

**7.** The method of convening a given surd into a rational
number on multiplication by another suitable surd is called rationalization of
surds. In this case the multiplying surd is called the rationalizing factor of
the given surd and conversely.

**8.** If a and b are
both rationals and √x and √y are both surds and a + √x = b + √y then a = b and
x = y

**9.** If a - √x = b - √y then a = b and x = y.

**10.** If a + √x = 0, then a = 0 and x = 0.

**11.** If a - √x = 0,
then a = 0 and x = 0.

**11 and 12 Grade Math**

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