5th roots | Mathematics I | High School Math | Khan Academy

TL;DR

Learn how to calculate fifth roots using factoring and trial and error methods.

Transcript

• [Instructor] Let's see if we can calculate the fifth root of 32. So, like always, pause the video and see if you can figure this out on your own. So, let's just remind ourselves what a fifth root is. So, if x is equal to the fifth root of 32, that's the same thing as saying x to the fifth power is equal to 32. So, we have to find some number wher... Read More

Key Insights

• ☺️ The fifth root of a number x can be calculated by factoring x and looking for factors that appear five times.
• ✊ If factoring is challenging, trial and error can be used by guessing values and checking their fifth powers.
• ✋ Calculating higher-order roots without a calculator can be more complex.
• 🏆 Divisibility tests, such as the sum of digits test for divisibility by three, can help in factoring.
• ✊ Guessing values close to the solution and raising them to the fifth power can help narrow down the possible roots.
• 🧑‍🏭 It is easier to find the fifth root of numbers that can be factored into smaller factors.
• ✋ Understanding the concept of a fifth root is essential for solving higher-level mathematical problems.

Questions & Answers

Q: What is the fifth root of 32?

The fifth root of 32 is equal to 2. This can be found by factoring 32 into 2^5 or by trial and error using powers of numbers.

Q: How can you determine if a number is divisible by three?

You can test if a number is divisible by three by summing its digits and checking if the sum is divisible by three.

Q: How can trial and error be used to calculate fifth roots?

By trying different values and raising them to the fifth power, you can determine which value, when raised to the fifth power, equals the given number.

Q: What is the fifth root of 243?

The fifth root of 243 is equal to 3. This can be found by factoring 243 into 3^5 or by trial and error using different values and checking their fifth powers.

Summary & Key Takeaways

• The fifth root of a number x is the value that, when raised to the power of five, gives the number x.

• One way to calculate the fifth root is by factoring the number and checking for factors that appear five times.

• Another method is trial and error, where you guess values and raise them to the fifth power to check if they equal the given number.