Tell whether each number is a real number, rational number, irrational, interger, or whole number, and then order then from least to greatest.
( Square root sign) 49, 8, -( square root sign) 4, and -3.
Could someone explain to me how they found the answers to this?
58
*11
a.a number is decreased by the square4
To determine whether each number is a real number, rational number, irrational number, integer, or whole number, we need to understand the definitions of these terms.
1. Real Numbers: Real numbers include all numbers on the number line. This includes both rational and irrational numbers.
2. Rational Numbers: Rational numbers can be expressed as fractions or ratios of two integers. They can be written in the form p/q, where p and q are integers and q is not equal to zero. The result of dividing two integers is a rational number.
3. Irrational Numbers: Irrational numbers cannot be expressed as fractions, and their decimal representations neither terminate nor repeat. Examples of irrational numbers include square roots of non-perfect squares or numbers like pi or e.
4. Integer: Integers are whole numbers (both positive and negative) and zero. They do not include fractions or decimals.
5. Whole Numbers: Whole numbers are non-negative integers (positive integers and zero). They do not include negative numbers or fractions.
Now let's apply this information to each number in the given set and order them from least to greatest:
1. √49: The square root of 49 is a rational number because 49 is a perfect square (7 * 7 = 49). Therefore, √49 = 7, which is an integer and a whole number.
2. 8: The number 8 is a rational number because it can be expressed as 8/1, where both 8 and 1 are integers.
3. -√4: The negative square root of 4 is a rational number since 4 is a perfect square (2 * 2 = 4). Hence, -√4 = -2, which is an integer and a whole number.
4. -3: The number -3 is an integer and a whole number.
Now, let's order them from least to greatest:
-3 < -√4 < 8 < √49
Therefore, the numbers in ascending order are: -3, -√4, 8, √49.