Simplifying radicals can be a daunting task, especially when dealing with complex expressions like 98. However, by breaking it down into manageable steps, you can simplify even the most challenging radicals.
Understanding Radicals
Before we dive into the steps to simplify 98, let's take a moment to understand what radicals are and why they're important. Radicals, also known as roots, are mathematical expressions that represent a value that, when raised to a power, gives a specified result. In the case of 98, we're looking for a value that, when multiplied by itself 98 times, gives 98.
Step 1: Factor Out Perfect Squares
The first step to simplifying 98 is to factor out any perfect squares. A perfect square is a number that can be expressed as the square of an integer. In this case, we can factor out 4, which is a perfect square.
98 = 4 × 24.5
By factoring out the perfect square, we've reduced the complexity of the radical and made it easier to simplify further.
How to Factor Out Perfect Squares
To factor out perfect squares, look for numbers that can be expressed as the square of an integer. For example, 4 is a perfect square because it can be expressed as 2 × 2. When factoring out perfect squares, make sure to divide the number inside the radical by the perfect square.
Step 2: Simplify the Radical
Now that we've factored out the perfect square, we can simplify the radical further. We can rewrite 24.5 as 4.9 × 5.
98 = 4 × 4.9 × 5
Next, we can simplify the radical by taking the square root of 4.9 and 5.
98 = 4 × √(4.9) × √5
By simplifying the radical, we've reduced the complexity of the expression and made it easier to work with.
How to Simplify Radicals
To simplify radicals, look for numbers that can be expressed as the product of two or more factors. When simplifying radicals, make sure to take the square root of each factor.
Step 3: Combine Like Terms
The final step to simplifying 98 is to combine like terms. We can combine the square roots of 4.9 and 5.
98 = 4 × √(4.9 × 5)
By combining like terms, we've simplified the radical expression even further.
How to Combine Like Terms
To combine like terms, look for numbers that can be combined using basic arithmetic operations like addition, subtraction, multiplication, and division. When combining like terms, make sure to follow the order of operations.
What is a radical in math?
+A radical, also known as a root, is a mathematical expression that represents a value that, when raised to a power, gives a specified result.
How do I simplify radicals?
+To simplify radicals, factor out perfect squares, simplify the radical, and combine like terms.
What is a perfect square in math?
+A perfect square is a number that can be expressed as the square of an integer. For example, 4 is a perfect square because it can be expressed as 2 × 2.
By following these three steps, you can simplify even the most complex radicals. Remember to factor out perfect squares, simplify the radical, and combine like terms. With practice and patience, you'll become a pro at simplifying radicals in no time!