What is the PRODUCT RULE (multiplication) for ROOTS?
^{n}√a ^{. }^{n}√b = ^{n}√ab
and
^{n}√ab = ^{n}√a . ^{n}√b
What is the QUOTIENT RULE (division) for ROOTS?
^{n}√a / ^{n}√b = ^{n}√a/b
and
^{n}√a / b = ^{n}√a / ^{n}√b
Radical expressions that involve the sum and difference of the same two terms are called CONJUGATES. What does the "special product" tp multiply CONJUGATES?
( A + B ) ( A - B ) = A^{2} - B^{2}
Example:
( √11 + 5 ) ( √11 - 5)
= ( √11 )^{2} - 5^{2} = 11 - 25 = -14
How do you RATIONALIZE the DENOMINATOR? w/ 1 term in the denominator.
Its the process of rewriting a radical expression as an equivalent expression in which the denominator no longer contains any radicals.
Example:
4 / √7 = 4 / √7 . √7 / √7 = 4√7 / 7
How do you RATIONALIZE the DENOMINATOR? w/ 2 terms in the denominator.
You rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator.
Example:
9/ 7 - √5 = 9/ 7 - √5 ^{. }7 + √5 / 7 + √5
= 9 ( 7 + √5 ) / 7^{2} - ( √5)^{2}
= 9 ( 7 + √5 ) / 49-5 = 9 ( 7 + √5) / 44
^{ }^{ }
How do you solve a RADICAL EQUATION containg a SQUARE ROOT?
1. isolate the radical
2. square both sides.
3. solve the resulting equation
4. check proposed solutions in original equation. Solutions of the squared equation, but not the original equation, are called extraneous solutions.
***after you SQUARE both sides, use
(A-B)^{2} = A^{2} - 2(A)(B) + B^{2 }
^{}
What is the SQUARE ROOT PROPERTY?
If u is an algebraic expression and d is a positive real number, then u^{2} = d has exactly 2 solutions.
If u^{2} = d, then u = √d or u = -√d
equivalently,
If u^{2} = d, then u = + √d
What is the PYTHAGOREAN THEOREM?
What is the DISTANCE FORMULA?
To compute the distance between 2 points, find the square of the difference between the x-coordinates plus the square of the difference between the y-coordinates. The pricipal square root of this sum is the distance.
How do you COMPLETE the SQUARE?
if x2 + bx is a binomial, then by adding (b / 2)2, which is the square of half the coefficient of x, a perfect square trinomial will result.