Radicals

Radicals are mathematical expressions that contain a square root, cube root, or any other higher order root of a number. In algebra, radicals are used to solve equations and simplify expressions. Radicals can be added, subtracted, multiplied, and divided. In order to perform these operations, the radicals must be in their simplest form, called radical form. When adding or subtracting radicals, the radicals must have the same index and radicand. To multiply radicals, the indices are added and the radicands are multiplied. To divide radicals, the index of the dividend is divided by the index of the divisor and the radicand of the dividend is divided by the radicand of the divisor.

Radicals are often feared by students first encountering them in Algebra. This is usually because they have only seen radicals in geometry, where they represented things like square roots of numbers. In Algebra, however, radicals are much more versatile and can represent other things, like cube roots and even higher order roots. Additionally, radicals can be used in equations and solving equations with radicals usually requires using the properties of radicals.

Some of the main properties of radicals include:

• Radicals can be added and subtracted like any other number
• The product of two radicals is another radical
• The quotient of two radicals is another radical
• A radical can be raised to a power, which results in another radical
• A radical can be simplified by factors that are perfect squares
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To add or subtract radicals, the radicals must have the same number underneath the root sign. This is called the index or the radicand. When multiplying radicals, the radicals can have different indices, but the radicands must be the same. When dividing radicals, the radicals can have different indices, but the radicands must be the same. To raise a radical to a power, both the index and the radicand are raised to that power. For example, if you have the radical √9 and you raise it to the second power, you would get 9. To simplify a radical, you look for any factors that are perfect squares. For example, the radical √18 can be simplified to √9√2 because 9 is a perfect square.

Learning radicals can be difficult at first, but with some practice, it can become easier. It is important to be able to work with radicals because they show up often in mathematics and in real-world problems.