(x)slates

Radicals

When the square root of a number is squared, the result is the original number. The reason why it’s called square root has to do with the area of the square that you obtain when graphing the radicand on the coordinate plane.

In general, the principal square root of a number $a$ is the nonnegative number that, when multiplied by itself, equals $a$. It is written as a radical expression, with a symbol called a radical over the term called the radicand: $\sqrt a$.

Again, radicals also have their rules that help you speed up calculations by hand.

The extension of the square root is the nth root which states that if $a$ is a real number with at least one nth root, then the principal nth root of $a$, written as $\sqrt[n] a$, is the number with the same sign as $a$ that, when raised to the nth power, equals $a$. The index of the radical is n.

Rational exponents are another way to express principal nth roots. The general form for converting between a radical expression with a radical symbol and one with a rational exponent is

$$a^\frac{m}{n} = (\sqrt[n] a)^m = \sqrt[n]{a^m}$$


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