# What is a radical in algebra?

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Following is a knowledge on radicals which will help you to get solution to algebra problems. A radical is a root sign. Radicals require an index to define what root it is. With square roots, the two is generally left off. With cube roots (index of three) a 3 is written on top of the left side of the radical. The index tells how many times the root needs to be multiplied by itself to equal the radicand.
We can even generalize and find the nth root which would be a number multiplied by itself n times to equal the radicand.

Ex.

Square root of 9.
2 is the index and 9 is the radicand. The square root of 9 is 3. This means that 3 x 3 = 9

Cube root of 64.
3 is the index and 64 is the radicand. The cube root of 64 is 4. This means that 4 x 4 x 4 = 64
One last thing to think about, we can also write the index, for exampe 2 in the square root of 9, as a fractional exponent. So 9(1/2) is another way of writting the square root of 9 and 64(1/3) is another way of saying the cube root of 64.
Now the law of exponents say (am)n= amn so, if we have the square root of 9 raised to the power 2 we have
(91/2)2 = 9(2/2) =91 =9 which helps us to see how we relate square root and square of a number.

The concept of radical is very, very important in algebra. Among other reasons, it was proven by Ruffini, and more later more rigorously by Abel, in 1824, that quintic (and higher) equations cannot be solved in radicals. There are solutions to these higher equations, but these solutions require methods from numerical analysis or from the theory of elliptic functions, rather than algebraic factorization into radicals.

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Radicals were first used in 1525 in Die Cross. They were first usedby Christoff Rudolff, who was a German mathematician.

It is from Latin

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