Name the subset(s) of real numbers to which each number belongs. Then order the numbers from least to greatest. Square root of 105, -4, 4/3.
To determine the subset(s) of real numbers to which each number belongs, we need to consider their nature.
1. Square root of 105:
The square root of 105 belongs to the subset of real numbers. We know this because 105 is a positive number, and the square root of any positive number is a real number.
2. -4:
The number -4 belongs to the subset of real numbers since it is an integer and all integers are real numbers.
3. 4/3:
The number 4/3 belongs to the subset of real numbers. Any fraction or decimal number is considered a real number.
Now, to order the numbers from least to greatest:
We have -4, 4/3, and the square root of 105.
Arranging them in order, we get:
-4, 4/3, square root of 105.
Therefore, the numbers in ascending order are -4, 4/3, square root of 105.
To determine the subset(s) of real numbers to which each number belongs, we will look at their characteristics.
1. Square root of 105: The square root of a number is only defined if the number is non-negative. Since 105 is positive, the square root of 105 is a real number.
2. -4: Since -4 is a negative number, it is also a real number.
3. 4/3: 4/3 is a fraction, and fractions that are ratios of two integers are known as rational numbers. Therefore, 4/3 is a rational number and hence a real number.
Now, let's order the numbers from least to greatest:
-4 < 4/3 < √105
So, the numbers in increasing order are:
-4, 4/3, √105