Operations on Radical Expressions
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A radical expression is an expression that contains a square root symbol (√). The number or expression inside the square root symbol is called the radicand.
To add or subtract radical expressions, you need to have the same radicand under the same square root symbol. Then, you can add or subtract the numbers outside the square root symbol.
For example, to add √4 + √9, we can simplify both expressions to the same radicand, √9, and add the numbers outside the square root symbol:
√4 + √9 = √9 + √9 = 2√9
To multiply radical expressions, you can simply multiply the numbers outside the square root symbol and multiply the radicands inside the square root symbol.
For example, to multiply √2 * √3, we can multiply the numbers outside the square root symbol and multiply the radicands inside the square root symbol:
√2 _ √3 = √(2 _ 3) = √6
To divide radical expressions, you can use the property of division that states that dividing by a number is the same as multiplying by its reciprocal. So, you can invert the second radical expression and multiply the two expressions.
For example, to divide √16 / √4, we can invert the second radical expression and multiply:
√16 / √4 = √16 _ (1 / √4) = √16 _ √(1 / 4) = √16 _ √1/4 = √16 _ (1 / 2) = √16 / 2 = 2 / 2 = 1
These are some basic operations that can be performed on radical expressions. It's important to simplify the expressions as much as possible to make the calculations easier and more accurate.