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Level 179

Radical Expressions & Equations


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radical expressions
expressions which contain a radical, i.e., a square root
simplest radical form
all three are true: 1) radicand has no perfect-square factors other than 1; 2) radicand has no fractions; 3) denominator of a fraction has no radical
Radicand
the expression under a radical sign
rationalize a denominator containing a single radical term
multiply the numerator and denominator by the same radical expression
conjugates
the sum or difference of the same two terms
rationalize a denominator containing a sum or difference
multiply the numerator and denominator by the conjugate of the denominator
like radicals
radical expressions which have the same radicand
unlike radicals
radical expressions which do not have the same radicand
radical equation
an equation that has a variable in a radicand
extraneous solution
a solution to a radical equation that does not satisfy the original equation
square root function
a function that contains the independent variable in the radicand
sine of an angle
length of opposite leg/length of the hypotenuse
cosine of an angle
length of adjacent leg/length of the hypotenuse
tangent of an angle
length of opposite leg/length of the adjacent leg
trigonometric ratio
ratios of the sides of a right triangle, including sine, cosine and tangent
angle of elevation
The angle above horizontal that an observer must look to see an object that is higher than the observer. Note: The angle of elevation is congruent to the angle of depression due to the alternate interior angles theorem
angle of depression
The angle below horizontal that an observer must look to see an object that is lower than the observer. Note: The angle of depression is congruent to the angle of elevation due to the alternate interior angles theorem