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basic explanation:

To simplify a radical expression, first find the prime factorization of the number within the radical. Afterwards, find the prime factors that occurred x amount of times or more, where x is the value you enter to the left. With each of these prime factors, round their occurrences down to the nearest multiple of x. If there are no prime factors that occur x or more times, the radical is already simplified. For each prime factor that occurs x or more times, calculate the prime factor to the power of their rounded number of occurrences. Next divide the original number within the radical by each of these results. Then put each result within the radical being multiplied together along with the result of the last step. Finally, find the x root of each value within the radical except the last listed value (which should be the result of the step before last). Put the results being multiplied by each other outside the radical, following by the radical itself with the last value still in it.

in-depth explanation:

The process for simplifying a radical expressions is already explained in the basic explanation. This section provides an explanation of prime factorization for those unfamiliar with it. If you are already knowledgeable on this subject, you may skip this section.

he prime factorization of a number is the prime factors that multiply to equal the number being prime factorized. There can be multiple occurrences of one prime factor within a single prime factorization. For example, the prime factorization of 12 is 2 × 2 × 3. To find the prime factorization of a number, first decide whether the number is itself a factor. If it is, the prime factorization of the number is simply the number itself. Otherwise, you must divide the number being prime factorized by the closest prime number less than the number itself. If the remainder is 0, the divisor is part of the prime factorization of the number being prime factorized. Otherwise, the divisor is not part of the prime factorization of the number being prime factorized. Continue dividing the number being factorized by a prime number each time, going to the closest prime number below the most recent prime number, until you are out of prime numbers. When you hit this point, you have found the prime factorization.

practice problems:

To fully understand this concept, it is important to utilize your knowledge through problems. Rather than creating your own, you can simply use some of the ones from our collection of simplify radical expressions problems below. They are categorized into three different categories: easy, medium, and hard. It is recommended you begin with the easy problems and work your way up from there. If you are having difficulties solving any of the problems, you may use our simplify radical expressions calculator which will calculate the answer and provide steps on how the problem was solved. You may also use the calculator to check you got the correct answer.

Keep in mind that not all radical expressions can be simplified further.

easy:

1.) Simplify the following radical expression:^{2}√34

2.) Simplify the following radical expression:^{2}√23

3.) Simplify the following radical expression:^{2}√12

4.) Simplify the following radical expression:^{2}√45

5.) Simplify the following radical expression:^{2}√52

6.) Simplify the following radical expression:^{2}√18

7.) Simplify the following radical expression:^{2}√17

8.) Simplify the following radical expression:^{2}√30

9.) Simplify the following radical expression:^{2}√27

10.) Simplify the following radical expression:^{2}√46

medium:

1.) Simplify the following radical expression:^{3}√27

2.) Simplify the following radical expression:^{3}√57

3.) Simplify the following radical expression:^{3}√85

4.) Simplify the following radical expression:^{3}√580

5.) Simplify the following radical expression:^{3}√347

6.) Simplify the following radical expression:^{3}√688

7.) Simplify the following radical expression:^{3}√487

8.) Simplify the following radical expression:^{3}√424

9.) Simplify the following radical expression:^{3}√875

10.) Simplify the following radical expression:^{3}√878

hard:

1.) Simplify the following radical expression:^{4}√1,484

2.) Simplify the following radical expression:^{4}√2,438

3.) Simplify the following radical expression:^{4}√4,584

4.) Simplify the following radical expression:^{4}√3,569

5.) Simplify the following radical expression:^{4}√3,523

6.) Simplify the following radical expression:^{4}√1,480

7.) Simplify the following radical expression:^{4}√7,282

8.) Simplify the following radical expression:^{4}√12,348

9.) Simplify the following radical expression:^{4}√10,538

10.) Simplify the following radical expression:^{4}√63,348

- Simplify Radical Expressions Calculator
- Basic Explanation
- In-Depth Explanation
- Simplify Radical Expressions Practice Problems

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Enter problem to view work.

basic explanation:

To simplify a radical expression, first find the prime factorization of the number within the radical. Afterwards, find the prime factors that occurred x amount of times or more, where x is the value you enter to the left. With each of these prime factors, round their occurrences down to the nearest multiple of x. If there are no prime factors that occur x or more times, the radical is already simplified. For each prime factor that occurs x or more times, calculate the prime factor to the power of their rounded number of occurrences. Next divide the original number within the radical by each of these results. Then put each result within the radical being multiplied together along with the result of the last step. Finally, find the x root of each value within the radical except the last listed value (which should be the result of the step before last). Put the results being multiplied by each other outside the radical, following by the radical itself with the last value still in it.

in-depth explanation:

The process for simplifying a radical expressions is already explained in the basic explanation. This section provides an explanation of prime factorization for those unfamiliar with it. If you are already knowledgeable on this subject, you may skip this section.

he prime factorization of a number is the prime factors that multiply to equal the number being prime factorized. There can be multiple occurrences of one prime factor within a single prime factorization. For example, the prime factorization of 12 is 2 × 2 × 3. To find the prime factorization of a number, first decide whether the number is itself a factor. If it is, the prime factorization of the number is simply the number itself. Otherwise, you must divide the number being prime factorized by the closest prime number less than the number itself. If the remainder is 0, the divisor is part of the prime factorization of the number being prime factorized. Otherwise, the divisor is not part of the prime factorization of the number being prime factorized. Continue dividing the number being factorized by a prime number each time, going to the closest prime number below the most recent prime number, until you are out of prime numbers. When you hit this point, you have found the prime factorization.

practice problems:

To fully understand this concept, it is important to utilize your knowledge through problems. Rather than creating your own, you can simply use some of the ones from our collection of simplify radical expressions problems below. They are categorized into three different categories: easy, medium, and hard. It is recommended you begin with the easy problems and work your way up from there. If you are having difficulties solving any of the problems, you may use our simplify radical expressions calculator which will calculate the answer and provide steps on how the problem was solved. You may also use the calculator to check you got the correct answer.

Keep in mind that not all radical expressions can be simplified further.

easy:

1.) Simplify the following radical expression:

2.) Simplify the following radical expression:

3.) Simplify the following radical expression:

4.) Simplify the following radical expression:

5.) Simplify the following radical expression:

6.) Simplify the following radical expression:

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8.) Simplify the following radical expression:

9.) Simplify the following radical expression:

10.) Simplify the following radical expression:

medium:

1.) Simplify the following radical expression:

2.) Simplify the following radical expression:

3.) Simplify the following radical expression:

4.) Simplify the following radical expression:

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9.) Simplify the following radical expression:

10.) Simplify the following radical expression:

hard:

1.) Simplify the following radical expression:

2.) Simplify the following radical expression:

3.) Simplify the following radical expression:

4.) Simplify the following radical expression:

5.) Simplify the following radical expression:

6.) Simplify the following radical expression:

7.) Simplify the following radical expression:

8.) Simplify the following radical expression:

9.) Simplify the following radical expression:

10.) Simplify the following radical expression: