Select the correct description for each number set.(4 points) a) (25−−√, 9, −−−√64−−√ ) b) ( -2.4, 0, 3.1, 81−−√ ) c) (−23, 79, π2 ) d) (12−−√, 11−−√, π )
a) (25−−√, 9, −−−√64−−√ )
- The first number, 25−−√, is the square root of 25, which is 5.
- The second number, 9, is a whole number.
- The third number, −−−√64−−√, is the square root of 64, which is 8.
So the correct description for this number set is: 5, 9, 8.
b) ( -2.4, 0, 3.1, 81−−√ )
- The first number, -2.4, is a decimal number.
- The second number, 0, is a whole number.
- The third number, 3.1, is a decimal number.
- The fourth number, 81−−√, is the square root of 81, which is 9.
So the correct description for this number set is: -2.4, 0, 3.1, 9.
c) (−23, 79, π2 )
- The first number, −23, is a negative whole number.
- The second number, 79, is a positive whole number.
- The third number, π2, is the square of π.
So the correct description for this number set is: -23, 79, π².
d) (12−−√, 11−−√, π )
- The first number, 12−−√, is the square root of 12.
- The second number, 11−−√, is the square root of 11.
- The third number, π, is a irrational number representing the mathematical constant pi.
So the correct description for this number set is: √12, √11, π.
so, can you tell me what is rational and illrational
Sure! In mathematics, rational and irrational numbers are different types of real numbers.
Rational Numbers: A rational number can be expressed as a fraction p/q, where p and q are integers, and q is not equal to zero. In other words, a rational number can be written as a fraction or a ratio of two integers. Examples of rational numbers include: 1/2, 2/3, -5/4, 0.25, -3.
Irrational Numbers: An irrational number cannot be expressed as a fraction. It cannot be written as a ratio of two integers. Irrational numbers are non-repeating and non-terminating decimals. Examples of irrational numbers include: √2, π (pi), √3, e (Euler's number), φ (Golden ratio).
In summary, rational numbers can be expressed as fractions or ratios of integers, while irrational numbers cannot be expressed as fractions and are non-repeating and non-terminating decimals.
no between the numbers
Apologies for the confusion. To clarify:
Rational Numbers: Rational numbers are numbers that can be expressed as the quotient or fraction p/q, where p and q are integers and q is not equal to zero. They can be written as terminating decimals or repeating decimals. Rational numbers can also be written as whole numbers or integers since they can be expressed as a fraction with a denominator of 1. Examples of rational numbers include: 1/2, 0.75, -4, 5, 3.333...
Irrational Numbers: Irrational numbers are numbers that cannot be expressed as a fraction or the quotient of two integers. They are non-repeating and non-terminating decimals. Irrational numbers cannot be expressed as a ratio, and their decimal representation goes on forever without repeating any pattern. Examples of irrational numbers include: √2, √3, π (pi), e (Euler's number), φ (Golden ratio).
So, in the number sets mentioned:
a) The numbers (25−−√, 9, −−−√64−−√) contain both rational and irrational numbers. 25−−√ is the square root of 25, which is rational (5). −−−√64−−√ is the square root of 64, which is also rational (8). 9 is a rational whole number.
b) The numbers (-2.4, 0, 3.1, 81−−√) are all rational numbers. They can be expressed as decimals or whole numbers. 81−−√ is the square root of 81, which is rational (9).
c) The numbers (−23, 79, π2) contain both rational and irrational numbers. −23 and 79 are rational whole numbers. π2 represents the square of π, which is an irrational number.
d) The numbers (12−−√, 11−−√, π) contain both rational and irrational numbers. 12−−√ and 11−−√ represent the square roots of 12 and 11, respectively, which are irrational numbers. π (pi) is also an irrational number.