We write the nth root of "r" as formula_3. If "n" is 2, then the radical expression is a square root. If it is 3, it is a cube root. Other values of n are referred to using ordinal numbers, such as "fourth root" and "tenth root".
For example, formula_4 because formula_5. The 8 in that example is called the radicand, the 3 is called the index, and the check-shaped part is called the radical symbol or radical sign.
Roots and powers can be changed as shown in formula_6.
The product property of a radical expression is the statement that formula_7. The quotient property of a radical expression is the statement formula_8.
This is an example of how to simplify a radical.
If two radicals are the same, they can be combined. This is when both of the indexes and radicands are the same.
This is how to find the perfect square and rationalize the denominator.
Isle of Portland
The Isle of Portland is an island in Dorset in the south of England. Portland is south of the resort of Weymouth. 13,000 people live there. It is where the famous Portland limestone was originally found.
In 2012, the sailing in the Olympics will take place on Portland and in Weymouth.
Weymouth, Dorset
Weymouth is a resort town in Dorset on the south coast of England. 52,000 people live in the town. Thousands of tourists have holidays there, because it is by the sea. In summer it is sometimes sunny and warm and there is lots to do. The sailing in the 2012 Summer Olympics were held in Weymouth and on the Isle of Portland nearby.
Chrysanthemum
Chrysanthemums are a genus ("Chrysanthemum") of about 30 species of perennial flowering plants in the family Asteraceae, from Asia and northeast Europe.
Flagship
A flagship is the ship used by the officer who commanded a group of naval ships. The term comes from the custom of the commanding officer to fly a special flag to show he was present.
Used in this way, "flagship" is normally a temporary name; the flagship is wherever the officer is flying his flag. However, admirals have always needed a special place; a meeting room large enough to hold all the captains of the fleet, and a place for the admiral's staff to make plans and draw up orders.
Over the years, the term "flagship" has been borrowed by other industries. These include broadcasting, automobiles, cell phones, and others to mean their core products or services.
European magpie
The European magpie ("Pica pica") is a bird that lives in Europe, much of Asia, and northwest Africa. It is one of several birds in the crow family named as magpies.
In Europe, "magpie" is used by English speakers to call the European magpie; it is the only magpie in Europe outside the Iberian Peninsula.
Sui generis
Sui generis (pronounced or ) is a term from Latin. It can be translated to "Of (his/her/its) own kind". It basically means that something has very special characteristics. They are so special, that the thing cannot really be compared to anything else. It is used in various contexts. The term was invented by philosophers. What they originally wanted to say was that an idea is so specific as to be unique, that it cannot really be part of a broader concept.
When lawyers talk about something being "sui generis", they mean that something is unique. It cannot be compared. With intellectual property, a design can be "sui generis".
The European Union is something that has come to be in the last few years. In some ways it is like state in others like a confederation of states or an international organisation. It is mostly classified as "sui generis".
In the sociology of Emile Durkheim, "sui generis" is used to illustrate his theories on social existence. He says that society, as it was there before any living individual was born, is independent of all individuals. His "sui generis" (its closest English meaning in this sense being 'independent') society will furthermore continue its existence after the individual ceases to interact with it.
Meryl Streep was praised in a "Wall Street Journal" review of "The Devil Wears Prada": "(her) pitch-perfect portrayal of Miranda is "sui generis", with a dramatic existence of its own, as unique and memorable as, say, a Bette Davis character."
Martin Kettle in "The Guardian" said about hung parliaments: "Each is "sui generis", dependent on the particular parliamentary arithmetic, inter-party momentum and surrounding political circumstances."
"Slate" has used the term several times; one article discussed the unique variations of French Rose Champagne: "Grower Champagnes are wines made by small farmers in the Champagne region who, bucking convention, choose to craft their own wines rather than sell their grapes to the major Champagne houses. Typical of farmer fizzes, the grower rosés are utterly "sui generis"—in a few cases almost freakishly so."
A CNN "The Marquee" post said about James Brown, "I can't even begin to talk about his importance. He was "sui generis"."
Political commentator Dick Morris referred to the intense public interest in the 2008 US Presidential race as "clearly sui generis, and anything can happen."
Regular polygon
A regular polygon is a polygon which is both equilateral (which means all its sides have the same length) and equiangular (which means that all its angles are the same).
The simplest examples of regular polygons are:
Straightedge and compass construction
Straightedge and compass construction, also known as ruler-and-compass construction, is drawing of lengths, angles or shapes using only a ruler and compass.
Some things cannot be drawn this way. For example, there are only 32 regular polygons with an uneven number of sides which are known to be constructible. It has been proven that a square with the same area as the area of a circle cannot be constructed. This is called "Squaring the circle".
Carnation
A carnation is a type of flower. It has been grown for so many years, we are not sure where it came from.
Air Force One
Air Force One is the air traffic call sign (name) of any U.S. Air Force aircraft carrying the President of the United States.
The president usually flies in one of the two specially changed Boeing 747 jumbo jets (airplane) kept by the United States Air Force.
They are only called Air Force One when the President is on board. Otherwise it is called by its number like any other airplane.
When Richard Nixon resigned as President in 1974 he flew back to his home in California in Air Force One, but halfway to California he stopped being President and the airplane was then given a new name, SAM (Special Air Mission) 2700.
Incubus
In the Middle Ages, people in Europe believed that Incubi (one Incubus, several Incubi) were male demons. There were also female demons, called succubi. They lay on sleeping people, to have sexual intercourse with them. They would also do this to make other incubi. While they had sex with their victim, they drained its energy to sustain themselves. Sometimes, having sex with an incubus may result in a child, as in the legend of Merlin. Some sources say that the incubus may be identified by its unnaturally cold penis. Religious tradition holds that repeated intercourse with such a spirit by either males or females may result in bad health, or even death.
People have come up with different explanations for the incubus legends. In the Middle Ages, people worried a lot about sin, especially sexual sins of women. Victims may have been experiencing waking dreams or sleep paralysis. Also, nocturnal arousal, orgasm or nocturnal emission could be explained by the idea of creatures causing an otherwise guilt-producing and self-conscious behavior. The influence of incubi could also have been used to explain how pregnancies happen outside marriage; such pregnancies were often "unexplainable".and unnoticed