x2 = aa > 0
Square root
Properties of square roots
Adding, subtracting, multiplying and dividing square roots
Rationalizing a denominator
Quadratic equation  x2 = aa > 0
The quadratic equation x2 = a has two solutions which are opposite numbers only if a > 0.
If a = 0 then there is a repeated solution zero, and if  a < 0 then there are no solutions in the set of real numbers.
The solutions are also called the roots or zeros of the quadratic equation.
 Examples: a)   x2 = 16 b)   (x - 5)2 = 49 x2 - 42 = 0 (x - 5)2 - 72 = 0 (x - 4) · (x + 4) = 0 [(x - 5) - 7] · [(x - 5) + 7] = 0 x - 4 = 0    =>    x1 = 4 (x - 5) - 7 = 0    =>    x1 = 12 x + 4 = 0    =>    x2 = - 4 (x - 5) + 7 = 0    =>    x2 = -2
Square root
 The principal square root of a nonnegative real number a, denoted represents the nonnegative real
number x whose square (the result of multiplying the number by itself) is a, that is
The number a under the root sign is called the radicand.
As the square root is defined only when its radicand is a nonnegative number therefore,
 for example, the expression makes sense only if  x - 5 > 0, that is, only if x > 5.
Since the positive square root of a positive real number is called the principal square root this is why the square root of say 16, is taken as +4 despite the fact that the square of -4 is also 16
That is, by the square root of a, where a is a nonnegative number, we should mean, the positive square root of a.
The reason for taking the principal square root as the value of a square root of a positive real number, lies in the definition of a function f which requires that for each x in the domain there is at most one pair (x, y) in the codomain (where a set of ordered pairs (x, y) represents the graph of the function f ).
As a2 > 0 whether a > 0 or a < 0 we write
 Examples:
Properties of square roots
 Properties Examples
Adding, subtracting, multiplying and dividing square roots
 Examples:
Rationalizing a denominator
Rationalizing a denominator is a method for changing an irrational denominator into a rational one.
 Examples:
 To rationalize a denominator or numerator of the form multiply both numerator
 and denominator by a conjugate, where are conjugates of each other.
Intermediate algebra contents
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