Algebra: Chapter 11, Lesson 3, page 349.
Simplifying Radical Expressions
REMEMBER: `sqrt(x^2) = (x^2)^(1/2) = x^(2 * (1/2)) = x`. The `sqrt` is just a variable, expression or constant raised to the `1/2` power!
It’s easy to simplify radicals.
You can break up numbers and variables, because multiplication is commutative.
If asked to find the `sqrt(100)` , we could break up `sqrt(100)` into `sqrt(25)⋅sqrt(4)`. We know that the `sqrt(25)=5` and the `sqrt(4)=2`, then the `sqrt(100)= 5⋅2 = 10`. You can do the same with variables that have exponents.
If asked to find the `sqrt` of a variable with even exponents, `sqrt(x^6)` for example, the answer is just the variable with the exponent divided in 2.
So for `sqrt(x^6)`, the answer is `x^3`.
If the variable has odd exponents, like `sqrt(x^27)`, convert that to `sqrt(x^26)⋅sqrt(x^1)` and then take the `sqrt(x^26)⋅sqrt(x^1) =(x^13)⋅sqrt(x)`.
See these examples (1/2 way down the page) too.