1.
What's the most crucial symbol used under this topic?
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.
2.
What represents square root?
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 √.
3.
What is a rational exponent?
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.
4.
What's the relationship between rational exponents and radicals?
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.
5.
Numerators in fractional exponents start from where?
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.
6.
Rewriting a radical entails one of the following
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.
7.
Where, in the following do you use fractional exponents?
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.
8.
Which one is true about rational exponents and radicals?
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.
9.
Which number correctly represents cube root?
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.
10.
Which one is the radical sign in this topic?
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.