- What if we put a constant and a variable inside the radical?
- ⁿ√ab = ⁿ√a × ⁿ√b
- For example we have square root of 81x². If we want to simplify it using this method, we are going to separate the two values and get the square root. Finally, multiply the two values together.
- 3. √81x²= √81 × √x² = 9x
- ⁿ√a/b = ⁿ√a/ⁿ√b
- Now let us move on the third law of radicals. this law states that when finding the nth root of fractions, you can distribute the root in the numerator and denominator. Let us look at the examples. Now what is the answer in number 3?
- 1. ³√(7/5) = ³√7/³√52. √(xy/5) = √xy/√53. ³√(64/125) = ³√64/³√125
- The answer is 4/5
- Good!
- ⁿ√ᵐ√a= ᵐⁿ√a
- 1. ³√²√7 =⁽³⁾⁽²⁾√7 = ⁶√72. ⁵√⁴√21 = ⁽⁵⁾⁽⁴⁾√21 = ²⁰√213. ³√²√729 =
- Now let us discuss the final law. It states that when there are root inside a root, you can multiply the indexes to simplify. Look at the examples presented at the board. Then, solve number three here on the board.
- ⁿ√ᵐ√a=ᵐⁿ√a
- ²√³√729=⁽³⁾⁽²⁾√729 = ⁶√729 = 3
- Very good! Now that is our class for today. Thank you and good bye!