Surds

If ‘a’ be real number and ‘n’ be positive integer such that a^1/n is an irrational then a^1/n is called surd of order ‘n’.

Rules:

1. ⁿ√a = a^1/n
2. ⁿ√ab = ⁿ√a × ⁿ√b
3. ⁿ√a/b = ⁿ√a / ⁿ√b
4. (ⁿ√a)ⁿ = a
5. ^m√ⁿ√a = ^mn√a
6. (ⁿ√a)^m = ⁿ√a^m

Exercise

1. Find the value of (36)^1/6.
2. Find the value of √50 + √98.
3. Find the value of 2³√40 - 4³√320 + 3³√625 - 3³√5
4. Find the value of ³√2 × ⁶√3 × √5.
5. Find the smallest among the following:
   ³√3, ³√2, ²√2, ³√4
6. Find the largest among the following:
   ³√4, ⁴√6, ⁶√15, ¹²√245

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