Simplifying radicals can be a bit tricky, but don't worry, I'm here to guide you through it. Let's break down the process into 3 easy steps to simplify 128 into radical form.
First, let's understand what radicals are. Radicals, also known as roots, are a way to express a number as a product of a base and an exponent. In this case, we're dealing with the square root of 128.
Step 1: Find the Prime Factorization of 128
To simplify radicals, we need to find the prime factorization of the number under the radical sign. Prime factorization is the process of breaking down a number into its prime factors.
The prime factorization of 128 is:
128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^7
Step 2: Identify the Perfect Square Factor
Now, let's look for a perfect square factor in the prime factorization of 128. A perfect square factor is a factor that has an even exponent.
In this case, we have:
2^7 = 2^6 × 2
We can see that 2^6 is a perfect square factor (2^2 = 4), and the remaining factor is 2.
Step 3: Simplify the Radical
Now that we've identified the perfect square factor, we can simplify the radical:
√128 = √(2^6 × 2) = √(2^2 × 2^4 × 2) = √(4 × 16 × 2) = √(64 × 2) = √64 × √2 = 8√2
And there you have it! We've simplified 128 into radical form in 3 easy steps.
Simplifying radicals is an important concept in algebra, and it's used extensively in various mathematical operations. By following these 3 easy steps, you can simplify any radical expression with confidence!
What's Next?
Want to practice simplifying radicals? Try simplifying these numbers:
- √240
- √320
- √405
Take your time, and remember to follow the same steps: find the prime factorization, identify the perfect square factor, and simplify the radical.
Happy math-ing!
Do you have any questions about simplifying radicals? Share them in the comments below, and I'll be happy to help!
What is a radical in math?
+A radical in math is a symbol used to represent the square root or nth root of a number. It's a way to express a number as a product of a base and an exponent.
How do I simplify radicals?
+To simplify radicals, follow these steps: (1) find the prime factorization of the number under the radical sign, (2) identify the perfect square factor, and (3) simplify the radical by extracting the perfect square factor.
What is the difference between a radical and a root?
+A radical and a root are often used interchangeably, but technically, a radical is a symbol used to represent a root. A root, on the other hand, is the actual value of the expression under the radical sign.