Simplifying Radical Expressions: Adding and Subtracting
When it comes to simplifying radical expressions, adding and subtracting can sometimes be intimidating. However, fear not! This article will walk you through the process step-by-step, ensuring that you can confidently tackle any radical expression involving addition or subtraction.
The first key to simplifying radical expressions is understanding the basics. A radical expression consists of a radical symbol (√) and a radicand, which is the number or expression underneath the radical symbol. To simplify, we aim to find the factors that are perfect squares (for square roots) or perfect cubes (for cube roots) of the radicand.
Let’s apply this knowledge to an example:
Consider the expression √18 + √8. To begin simplifying, we break down each radicand into its prime factorization:
√18 = √(2 × 3 × 3) = √(2 × 32) = 3√2
√8 = √(2 × 2 × 2) = √(23) = 2√2
Now, we can add the simplified expressions:
3√2 + 2√2 = 5√2 (combining like terms)
And that’s it! Our final result is 5√2.
To further illustrate, let’s consider a subtraction example:
√32 – √2
Again, we factorize the radicands:
√32 = √(2 × 2 × 2 × 2 × 2) = √(25) = 2√2
√2 remains as is since it cannot be further simplified.
Subtracting these expressions:
2√2 - √2 = √2 (combining like terms)
Our simplified result is √2.
To summarize, simplifying radical expressions involving addition or subtraction requires breaking down the radicands into their prime factors and simplifying them individually. Once simplified, we can combine like terms by adding or subtracting the resulting expressions.
In conclusion, simplifying radical expressions involving addition and subtraction may seem complex at first, but with a solid understanding of the process, it becomes much simpler. By following the steps outlined in this article, you can confidently navigate through any radical expression problem and simplify it with ease.
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