Algebra: Chapter 11-3, p349
Simplifying Radical Expressions
`sqrt(x^2)` = square root `(x^2)` = `x`
Its 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 `100` into `25 * 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 `x^27`, convert that to `(x^26)*(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.
Math-8: Chapter 11-6, p 578
Similar Triangles
If 2 triangles are similar, then the corresponding angles are congruent. If 2 triangles are similar, them their corresponding sides are proportional. Similar triangles have the SAME SHAPE but not necessarily the SAME SIZE are similar figures. You can use proportions to find the measures of the sides of similar triangles when some measures are known.