What's the relationship between rational exponents and radicals?

Rational exponents and radicals are different ways of expressing the same thing

Rational exponents and radicals are progressive equations used in resolving bigger problems

They are separate entities that cannot work together

Rewriting a radical entails one of the following

Radicand becomes numerator while root becomes denominator

Radicand is multiplied by the root

Which one is true about rational exponents and radicals?

They provide different ways to solve certain/specific problems

They don't make use of numerators or denominators

What Do You Know About Rational Exponents & Radicals?

Approved & Edited by ProProfs Editorial Team

The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.

Learn about Our Editorial Process

| By Livyn

Livyn

Community Contributor

Quizzes Created: 304 | Total Attempts: 147,240

Questions: 10 | Attempts: 268 | Updated: Mar 21, 2023

Questions

Settings

Create your own Quiz

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

What Do You Know About Rational Exponents & Radicals? - Quiz

In as much as you know a bit about the topic, you'll be completely fine. If you don't, then you'll learn more.

Questions and Answers

1.

What's the most crucial symbol used under this topic?
- A.
  
  Division
- B.
  
  Square roots
- C.
  
  Square of a number
- D.
  
  Cube of a numbee
Correct Answer
B. Square roots

Explanation
The most crucial symbol used under this topic is square roots. Square roots are important in mathematics as they help us find the value that, when multiplied by itself, gives the original number. They are commonly used in various mathematical operations and equations, such as solving quadratic equations or finding the length of the sides of a square. Understanding square roots is essential for grasping more advanced mathematical concepts and problem-solving.

Rate this question:
2.

What represents square root?
- A.
  
  √
- B.
  
  π
- C.
  
  °
- D.
  
  |
Correct Answer
A. √

Explanation
The symbol √ represents the square root. It is commonly used in mathematics to indicate the principal square root of a number. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 multiplied by itself equals 9. Therefore, the correct answer is √.

Rate this question:
3.

What is a rational exponent?
- A.
  
  A number
- B.
  
  A number greater than 10
- C.
  
  A whole number
- D.
  
  A fraction
Correct Answer
A. A number

Explanation
A rational exponent is a number that can be expressed as a fraction, where the numerator is an integer and the denominator is a positive integer. It represents the power to which a number is raised.

Rate this question:
4.

What's the relationship between rational exponents and radicals?
- A.
  
  Rational exponents and radicals are progressive equations used in resolving bigger problems
- B.
  
  They're in the same form
- C.
  
  Rational exponents and radicals are different ways of expressing the same thing
- D.
  
  They are separate entities that cannot work together
Correct Answer
C. Rational exponents and radicals are different ways of expressing the same thing

Explanation
Rational exponents and radicals are different ways of expressing the same thing. This means that they both represent the same mathematical concept, but are written in different forms. Rational exponents involve writing the exponent as a fraction, while radicals involve using a root symbol. However, both methods can be used to calculate the same result. Therefore, rational exponents and radicals are essentially interchangeable and can be used interchangeably depending on the preference or convenience of the mathematician.

Rate this question:
5.

$Numerators in fractional exponents start from where? - ProProfs$

Numerators in fractional exponents start from where?
- A.
  
  0
- B.
  
  1
- C.
  
  4 above only
- D.
  
  1.5
Correct Answer
B. 1

Explanation
The numerator in fractional exponents represents the power to which the base is raised. In this case, the correct answer is 1 because the numerator starts from 1. This means that the base will be raised to the power of 1, resulting in the base itself.

Rate this question:
6.

Rewriting a radical entails one of the following
- A.
  
  Root is multiplied by 2
- B.
  
  Root is squared
- C.
  
  Radicand becomes numerator while root becomes denominator
- D.
  
  Radicand is multiplied by the root
Correct Answer
C. Radicand becomes numerator while root becomes denominator

Explanation
When rewriting a radical, the radicand (the number inside the square root) becomes the numerator of a fraction, while the root (the number outside the square root) becomes the denominator. This is a common method used to simplify radicals and make them easier to work with.

Rate this question:
7.

$Where, in the following do you use fractional exponents? - ProProfs$

Where, in the following do you use fractional exponents?
- A.
  
  None
- B.
  
  Calculus
- C.
  
  Factorization
- D.
  
  Trigonometry
Correct Answer
B. Calculus

Explanation
Fractional exponents are commonly used in calculus to represent roots and powers of numbers. In calculus, fractional exponents are used to express derivatives and integrals of functions, as well as to solve equations involving exponential and logarithmic functions. This is because fractional exponents allow for more precise and flexible calculations compared to whole number exponents. Therefore, the correct answer is Calculus.

Rate this question:
8.

Which one is true about rational exponents and radicals?
- A.
  
  They limit calculations a lot
- B.
  
  They provide different ways to solve certain/specific problems
- C.
  
  They don't make use of numerators or denominators
- D.
  
  They leave remainders
Correct Answer
B. They provide different ways to solve certain/specific problems

Explanation
Rational exponents and radicals provide different methods to solve specific problems. Rational exponents allow us to express radicals in a fractional form, which can simplify calculations and make them more manageable. This alternative approach can be particularly useful when dealing with complex equations or expressions involving roots. By utilizing rational exponents, we can transform a radical into a more convenient form and apply algebraic operations more easily. Therefore, rational exponents and radicals offer distinct techniques to tackle specific mathematical problems.

Rate this question:
9.

Which number correctly represents cube root?
- A.
  
  3
- B.
  
  2
- C.
  
  4
- D.
  
  2.8 (approximately 3)
Correct Answer
A. 3

Explanation
The number 3 correctly represents the cube root because when you multiply 3 by itself three times (3 x 3 x 3), you get the cube of 27. Therefore, the cube root of 27 is 3.

Rate this question:
10.

Which one is the radical sign in this topic?
- A.
  
  ÷
- B.
  
  |
- C.
  
  °
- D.
  
  √
Correct Answer
D. √

Explanation
The radical sign, represented by √, is the correct answer. It is used to indicate the square root of a number. The other symbols, ÷, |, and °, do not represent the radical sign and have different meanings.

Rate this question: