i tried doing as much of the squared stuff as possible but i couldnt do most of those terms

### sqaure roots

1. if b is a perfect square then b is rational 2. if b is a positive number then (b squared) is irrational 3. if b is negative number, then (b squared) is not a real number

### distance formula

distance-d-between the points with coordinates (x1, y1) and (x2, y2) d= (sqaured.) ( x2-x1)2 + (y2-y1)2

### product rule for square roots

the sq root of the product of two nonnegative is equal to the product of their square roots

### simplified form of a sq root

1. except for 1, the radicand has no perfect square factors 2. no fraction appears in the radicand 3. no radicand appears in the denominator

### simplifying sq roots

1. write the radicand as a product of the greatest perfect sqaure factor and one other factor. 2. use the product rule for square roots to write the expression as a product of sq roots 3. find the sq root of the perfect sq factor

### the quotation rule of sq roots

the sq root of the quotient of two numbers is equal to the quotient of their square roots

### the product rule for sq roots

the product of the sq roots of two nonnegative numbers is equal to the square root of the product of those numbers

### the quotient rule for sq roots

the quotient of two numbers is equal to the square root of the quotient of the two numbers

### rationalizing the denominator

process in which we change the denominator from a radical that represents an irrational number to a rational number

### rationalizing denominators

to rationalize a square root denominator, mulitply the numerator and denominator of the given fraction by the sq root that appears in its denominator, or by a sq root that makes a perfect sq radicand in the denominator

### solving radical equations

1. Isolate a radical term on one side of the equation 2. Square both sides of the equation 3. Solve the resulting equation 4. Check the possible solutions in the original equation. This step is required